Mathematics College

## Answers

**Answer 1**

Answer:

78%

Step-by-step explanation:

70 = 0.50 (62) + 0.50 (x)

70 = 31 + 0.5x

39 = 0.5x

x = 78

You must get at least a 78% on the test to have at least 70% in the class.

## Related Questions

The cost to ride a ferris wheel is $2.00 per person. The ferris wheel has a capacity of 64 people. The amount of money collected is a function of the number of people who ride on the ferris wheel. M(p)=2p the domain of this function is restricted to

### Answers

Answer:

D=[0, 64]

Step-by-step explanation:

The domain of a function is the interval of all possible values of the independent variable. In this situation, the independent variable is the number of people on the ferris wheel 'p'. Since the capacity is 64 people, the possible interval for 'p' is from 0 to 64 people. Therefore, the domain is;

D=[0, 64]

Assume that a sample is used to estimate a population proportion p. Find the margin of error E that corresponds to the given statistics and confidence level. Round the margin of error to four decimal places. In a clinical test with 2400 subjects, 720 showed improvement from the treatment. Find the margin of error for the 99% confidence interval used to estimate the population proportion.

### Answers

Answer: 0.0241

Step-by-step explanation:

The formula we use to find the margin of error :

, where z* = Critical value , n= Sample size and p = Sample proportion.

As per given , we have

n= 2400

Sample proportion of subjects showed improvement from the treatment:

Critical value for 99% confidence = z*= 2.576 (By z-table)

Now , the margin of error for the 99% confidence interval used to estimate the population proportion. :

[Round to the four decimal places]

Hence, the margin of error for the 99% confidence interval used to estimate the population proportion. =0.0241

The distribution of actual weights of 8-ounce wedges of cheddar cheese produced at a dairy is Normal with mean 8.1 ounces and standard deviation 0.2 ounces. A sample of 10 of these cheese wedges is selected. The distribution of the sample mean of the weights of cheese wedges is: approximately Normal, mean 8.1, standard deviation 0.2.

approximately Normal, mean 8.1, standard deviation 0.020.

It is not possible to tell because the sample size is too small.

approximately Normal, mean 8.1, standard deviation 0.063.

### Answers

Answer:

approximately Normal, mean 8.1, standard deviation 0.063.

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".

Let X the random variable weights of 8-ounce wedges of cheddar cheese produced at a dairy. We know from the problem that the distribution for the random variable X is given by:

We take a sample of n=10 . That represent the sample size.

What can we say about the shape of the distribution of the sample mean?

From the central limit theorem we know that the distribution for the sample mean is also normal and is given by:

approximately Normal, mean 8.1, standard deviation 0.063.

The distribution of grade point averages (GPAs) for medical school applicants of a certain year were approximately Normal, with a mean of 3.48 and a standard deviation of 0.36. Suppose a medical school will only consider candidates with GPAs in the top 20% of the applicant pool. An applicant has a GPA of 3.75. Does this GPA fall in the top 20% of the applicant pool?

### Answers

Z-table is also known as the standard normal distribution table. The student is among the top 20%.

What is a Z-table?

A z-table also known as the standard normal distribution table, helps us to know the percentage of values that are below (or to the left of the Distribution) a z-score in the standard normal distribution.

Since it is given that the mean GPA of the students is 3.48, while the standard deviation is 0.36, therefore, the GPA which is in the top 20% can be given as:

Thus, the minimum GPA a student needs to score to be in 20% of the class is 3.69.

As the score of the student is 3.75, therefore, the student is among the top 20%.

Learn more about Z-table:

brainly.com/question/6096474

Answer:

So the score that separates the bottom 80% of data from the top 20% is 3.783. Since the value obtained by the applicant is 3.75 a)=0.20" align="absmiddle" class="latex-formula"> (a)

(b)

Both conditions are equivalent on this case. We can use the z score in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.80 of the area on the left and 0.20 of the area on the right it's z=0.842. We can found this with the following excel code:"=NORM.INV(0.8,0,1)". On this case P(Z0.842)=0.2

If we use condition (b) from previous we have this:

But we know which value of z satisfy the previous equation so then we can do this:

And if we solve for a we got

So the score that separates the bottom 80% of data from the top 20% is 3.783. Since the value obtained by the applicant is 3.75

What is an equation of the line that is parallel to y=9-5x and passes though (0,8)?

### Answers

y = 8-5x

Step-by-step explanation:

When two lines are parallel, it means their gradients are the same.

from the given equation

y = 9-5x

and comparing with the general equation of a line

y = mx+c, where m is the gradient, and c is the y-intercept,

m = -5

you can form a line parallel to that using the points (0,8)

(y-8)/(x-0)= -5

this would give you

y = 8-5x

A TV station claims that 38% of the 6:00 - 7:00 pm viewing audience watches its evening news program. A consumer group believes this is too high and plans to perform a test at the 5% significance level. Suppose a sample of 830 viewers from this time range contained 282 who regularly watch the TV station’s news program. Carry out the test and compute the p-value.

### Answers

Answer:

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that regularly watch the TV station’s news program is significantly less than 0.38 .

Step-by-step explanation:

1) Data given and notation

n=830 represent the random sample taken

X=282 represent the people that regularly watch the TV station’s news program

estimated proportion of people that regularly watch the TV station’s news program

is the value that we want to test

represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the proportion is less than 0.38:

Null hypothesis:

Alternative hypothesis:

When we conduct a proportion test we need to use the z statisitc, and the is given by:

(1)

The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided . The next step would be calculate the p value for this test.

Since is a left tailed test the p value would be:

So the p value obtained was a very low value and using the significance level given we have so we can conclude that we have enough evidence to reject the null hypothesis, and we can said that at 5% of significance the proportion of people that regularly watch the TV station’s news program is significantly less than 0.38 .

A complex electronic device contains three components, A, B, and C. The probabilities of failure for each component in any one year are 0.01, 0.03, and 0.04, respectively. If any one component fails, the device will fail. If the components fail independently of one another, what is the probability that the device will not fail in one year?

### Answers

Answer:

0.9219 or 92.19%

Step-by-step explanation:

The probability that the device will not fail in one year is given by the joint probability that none of the three components will fail within the year. The individual probabilities of not failing are:

The joint probability is:

There is a 0.9219 or 92.19% probability that the device will not fail in one year.

The Adecco workplace insights survey sampled men and women workers and asked if they expected to get a raise or promotion this year (USA Today, February 16, 2012). Suppose the survey sampled 200 men and 200 women. If 104 of the men replied yes and 74 of the women replied yes, are the results statistically significant so that you can conclude a greater proportion of men expect to get a raise or a promotion this year? a. State the hypothesis test in terms of the population proportion of men and the population proportion of women.

b. What is the sample proportion for men? For women?

c. Use a 0.1 level of significance. What is the p-value and what is your conclusion?

### Answers

Answer:

a) Null hypothesis:

Alternative hypothesis: p_{W}" alt="p_{M} > p_{W}" align="absmiddle" class="latex-formula">

b) represent the proportion of men that replied yes

represent the proportion of women that replied yes

c)

3.018)= 0.0013" alt="p_v =P(Z>3.018)= 0.0013" align="absmiddle" class="latex-formula">

So the p value is a very low value and using the significance level given always so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men is significant higher than the proportion of female .

Step-by-step explanation:

1) Data given and notation

represent the number of men that replied yes

represent the number of women that replied yes

sample of male selected

sample of demale selected

represent the proportion of men that replied yes

represent the proportion of women that replied yes

z would represent the statistic (variable of interest)

represent the value for the test (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to check if the proportion for men that replied yes is higher than the proportion of women that replied yes:

Null hypothesis:

Alternative hypothesis: p_{W}" alt="p_{M} > p_{W}" align="absmiddle" class="latex-formula">

We need to apply a z test to compare proportions, and the statistic is given by:

(1)

Where

3) Calculate the statistic

Replacing in formula (1) the values obtained we got this:

4) Statistical decision

For this case we don't have a significance level provided , but we can calculate the p value for this test.

Since is a one right tailed test the p value would be:

3.018)= 0.0013" alt="p_v =P(Z>3.018)= 0.0013" align="absmiddle" class="latex-formula">

So the p value is a very low value and using the significance level given always so we can conclude that we have enough evidence to reject the null hypothesis, and we can say the the proportion of men is significant higher than the proportion of female .

Each car in a sample of seven cars was tested for nitrogen-oxide emissions (in grams per mile), and the following results were obtained. 0.07, 0.11, 0.15, 0.13, 0.12, 0.07, 0.13 a. Assuming that this sample is representative of cars in use, construct a 95% confidence interval estimate of the mean amount of nitrogen-oxide emissions for all cars.

### Answers

Answer:

The 95% confidence interval would be given by (0.0825;0.1395)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

Data: 0.07, 0.11, 0.15, 0.13, 0.12, 0.07, 0.13

We can calculate the sample mean and deviation with the following formulas:

represent the sample mean for the sample

population mean (variable of interest)

s=0.0308 represent the sample standard deviation

n=7 represent the sample size

2) Confidence interval

The confidence interval for the mean is given by the following formula:

(1)

In order to calculate the critical value we need to find first the degrees of freedom, given by:

Since the Confidence is 0.95 or 95%, the value of and , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,6)".And we see that

Now we have everything in order to replace into formula (1):

So on this case the 95% confidence interval would be given by (0.0825;0.1395)

Suppose that the proportion of young adults who read at least one book per month is 0.15, and this proportion is the same in Boston and New York. Suppose that samples of size 400 are randomly drawn from each city. The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score) is _______.

### Answers

Answer: 0.025

Step-by-step explanation:

The standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion is given by :_

, where = First population proportion.

= Second population proportion

= First sample size

= Second sample size

As per given , we have

Then ,

Hence, the standard deviation for the sampling distribution of differences between the first sample proportion and the second sample proportion (used to calculate the z score) is 0.025 .

The force exerted by an electric charge at the origin on a charged particle at a point (x, y, z) with position vector r = x, y, z is F(r) = Kr/|r|3 where K is a constant. Find the work done as the particle moves along a straight line from (4, 0, 0) to (4, 3, 4).

### Answers

Answer:

Step-by-step explanation:

The straight line path between point (a,b,c) and (l,m,n) is parametric by the expression

since we are giving point (4,0,0) and (4,3,4), the parametric equation is giving below

using the dot product system of multiplication, we have

t is between 0,1.

Next we define the line integral for work done which is express as

First we define the general expression for the force

If we substitute our parametric equation we arrive at

also we need to find the expression for dr

Now we substitute into the integral expression

using dot product we arrive at

let make a simple substitution so we can simplify the integral,

let assume

and changing setting the new upper and lower limit, we have

by simple integral we arrive at

Hence the workdone is

The function d(s) = –5s – 15 models the depth, in feet, of a rock that Dante dropped into a lake s seconds after he lost sight of the rock. What is the meaning of the x-intercept?

### Answers

Answer:

The x-intercept will tell you how many seconds have passed before Dante lost sight of the rock.

Step-by-step explanation:

The problem specifies that the function d(s) will model the depth in feet of a rock that Dante dropped into a lake s seconds after he lost sight of the rock.

In this case we are using an s instead of the x, so the x-intercept will represent a given time. We can find the x-intercept by setting the function equal to zero, like this:

-5s-15=0

when solving for s we get:

s=-3

This means that Dante dropped the ball into a lake 3 seconds before he lost sight of the rock. This is what the negative stands for, some time in the past.

So the x-intercept tells us the time it took for Dante to lost sight of the rock.

Many high school students take the SAT's twice; once in their Junior year and once in their Senior year. In a sample of 60 such students, the score on the second try was, on average, 30 points above the first try with a standard deviation of 14 points. Test the claim that retaking the SAT increases the score on average by more than 25 points. Test this claim at the 0.05 significance level.(a) The claim is that the mean difference is greater than 25 (μd > 25), what type of test is this?1. This is a two-tailed test.2. This is a right-tailed test.3. This is a left-tailed test.(b) What is the test statistic? Round your answer to 2 decimal places.td= _______(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0 (e) Choose the appropriate concluding statement.1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.2. There is not enough data to support the claim that retaking the SAT increases the score on average by more than 25 points. 3. We reject the claim that retaking the SAT increases the score on average by more than 25 points.4. We have proven that retaking the SAT increases the score on average by more than 25 points

### Answers

Answer:

what type of test is this?

2. This is a right-tailed test

(b) What is the test statistic?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____

First we need to calculate the degrees of freedom given by:

Now we can calculate the p value, since we have a right tailed test the p value is given by:

2.77) =0.0037" alt="p_v =P(t_{(59)}>2.77) =0.0037" align="absmiddle" class="latex-formula">

And we can use the following excel code: "=1-T.DIST(2.77,59,TRUE)"

(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0

1. reject H0

e) Choose the appropriate concluding statement.

1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

Step-by-step explanation:

Data given

represent the sample mean difference

represent the sample standard deviation

n=60 represent the sample size selected

represent the significance level

Confidence =1-0.05=0.95

System of Hypothesis

The system of hypothesis for this case are:

Null hypothesis:

Alternative hypothesis: 25" alt="\mu_d >25" align="absmiddle" class="latex-formula">

what type of test is this?

2. This is a right-tailed test

(b) What is the test statistic?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.P-value = _____

First we need to calculate the degrees of freedom given by:

Now we can calculate the p value, since we have a right tailed test the p value is given by:

2.77) =0.0037" alt="p_v =P(t_{(59)}>2.77) =0.0037" align="absmiddle" class="latex-formula">

And we can use the following excel code: "=1-T.DIST(2.77,59,TRUE)"

(d) What is the conclusion regarding the null hypothesis?1. reject H02. fail to reject H0

1. reject H0

e) Choose the appropriate concluding statement.

1. The data supports the claim that retaking the SAT increases the score on average by more than 25 points.

The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) of pounds with a standard deviation of pounds. In a recent study, a group of people who used this pill were interviewed. The study revealed that these people lost a mean of pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of individuals will be pounds or less?

### Answers

Answer:

Step-by-step explanation:

Assuming this info: The producer of a weight-loss pill advertises that people who use the pill lose, after one week, an average (mean) 1.8 of pounds with a standard deviation of 0.95 pounds. In a recent study, a group of 45 people who used this pill were interviewed. The study revealed that these people lost a mean of 1.92 pounds after one week. If the producer's claim is correct, what is the probability that the mean weight loss after one week on this pill for a random sample of individuals will be 1.92 pounds or less?

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Let X the random variable that represent the interpupillary distance (the distance between the pupils of the left and right eyes) of a population, and for this case we know the distribution for X is given by:

Where and

And let represent the sample mean, the distribution for the sample mean is given by:

On this case

We are interested on this probability

And the best way to solve this problem is using the normal standard distribution and the z score given by:

2) Solution to the problem

If we apply this formula to our probability we got this:

And we can find this probability on this way:

We can use the following excel code to find it:

"=NORM.DIST(0.847,0,1,TRUE)"

Using the chart, find the total amount and amount of interest paid in the following compound interest problems. $3,000 at 8% for 5 years.

### Answers

Answer:

The total amount paid was $3,828.85 and the amount of interest paid was $828.85

Step-by-step explanation:

The compound interest formula is given by:

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

Total amount

Interest paid

A - P = 3,828.85 - 3,000 = 828.85

The total amount paid was $3,828.85 and the amount of interest paid was $828.85

Answer:

Annually: Total Amount $4,407.98, Interest Amount $1,407.98

Semi Annually: Total Amount $4,440.73, Interest Amount $1,440.73

Quarterly: Total Amount $4,457.84, Interest Amount $1,457.84

Battery life for a hand-held computer is normally distrituted and has a population standard deviation of 8 hours. Suppose you need to estimate a confidence interval estimate at the 80% level of confidence for the mean life of these batteries. Determine the sample size required to have a margin of error of 0.332 hours. Round up to the nearest whole number

### Answers

Answer:

Sample size= 956

Step-by-step explanation:

Hello!

You need to construct an 80% CI for the average life of batteries. (hours)

The study variable is:

X: Lifespan of a battery.

X~N(μ; σ²)

The population standard devition isσ= 8

The interval to estimate the population mean follows the structure:

"Point estimator" ± "margin of error"

X[bar] ± * (σ/√n)

X[bar] is the sample mean

* (σ/√n) is the margin of error of the interval (d)

Using the margin of error you can calculate the sample size:

d= * (σ/√n)

n= (σ* )²

n=

n= 955.77 ≅ 956

I hope it helps!

Elana spent $25 for two shirts that each cost the same amount of money. the shirts were marked $4.00 off the original price. the equation 2(p-4)=25 can be solved to find p the original price of the shirts . What was the original price ? A.10.50

B.16.50

C.14.50

D.8.50

which one

### Answers

Answer:

B.16.50

Step-by-step explanation:

2 (p - 4)=25

2p - 8 = 25

2p = 25 + 8

2p = 33

dividing the equation by 2

p = 16.50

Answer: B. 16.5

Step-by-step explanation:

2(p-4) =25.

-Divide both sides by 2 to make the expression simple.

- you are left with :

P-4=12.5.

- to make the unknown value (P) subject of the expression, we take 4 to the other side of the expression and that makes it positive.

- P= 12.5+4

P=16.5(Ans)

Suppose that a fast food restaurant decides to survey its customers to gauge interest in a breakfast menu. After surveying multiple people, the restaurant created a 95% confidence interval for the proportion of customers interested in a breakfast menu. The confidence interval is ( 0.521 , 0.597 ) . Use the confidence interval to find the point estimate

### Answers

Answer:

So for our case then

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

The population proportion have the following distribution

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and . And the critical value would be given by:

The confidence interval for the mean is given by the following formula:

For our case we have the interval already given (0.521;0.597)

So we can find the margin of error from this, first we need to find the width of the interval:

And then the margin of error is given by:

Now we can find the point of estimate subtracting the margin of error tot he upper limit or adding the margin of error to the lower limti like this:

So for our case then

Unfortunately, arsenic occurs naturally in some ground water†. A mean arsenic level of µ = 8.0 parts per billion (ppb) is considered safe for agricultural use. A well in Texas is used to water cotton crops. This well is tested on a regular basis for arsenic. A random sample of 36 tests gave a sample mean of x = 7.3 ppb arsenic, with s = 2.4 ppb. Does this information indicate that the mean level of arsenic in this well is less than 8 ppb? Use a = 0.05.(a) What is the level of significance?State the null and alternate hypotheses.H0: µ < 8 ppb; H1: µ = 8 ppb H0: µ > 8 ppb; H1: µ = 8 ppb H0: µ = 8 ppb; H1: µ ? 8 ppb H0: µ = 8 ppb; H1: µ > 8 ppb H0: µ = 8 ppb; H1: µ < 8 ppb(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.The standard normal, since the sample size is large and s is known. The standard normal, since the sample size is large and s is unknown. The Student's t, since the sample size is large and s is unknown. The Student's t, since the sample size is large and s is known.What is the value of the sample test statistic? (Round your answer to three decimal places.)(c) Find the P-value. (Round your answer to four decimal places.)Sketch the sampling distribution and show the area corresponding to the P-value.(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?At the a = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant. At the a = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant. At the a = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.(e) Interpret your conclusion in the context of the application.There is insufficient evidence at the 0.05 level to reject the claim that the mean level of arsenic in the well is not less than 8 ppb. There is sufficient evidence at the 0.05 level to reject the claim that the mean level of arsenic in the well is not less than 8 ppb.

### Answers

Answer:

Check the explanation below.

Step-by-step explanation:

Hello!

The study variable is:

X: Arsenic level of well water (ppb)

If the mean concentration of arsenic is 8 ppb then the water is considered safe to use for agricultural use.

In texas a sample of 36 tests for arsenic was taken to see if the average level of arsenic of the water well is less than 8 ppb, symbolically μ < 8

The hypothesis is:

a)

H₀: μ ≥ 8

H₁: μ < 8

Level of significance is α: 0.05

b)

To study the population mean the variable needs to have at least a normal distribution. If the information of the sample was available we could make a normality test to check if it's distribution is normal or not. Since the Students t cannot be used unless the variable has a normal distribution, we cannot choose this statistic to make the hypothesis test, the same happens with the standard normal, if the condition of a variable with normal distribution is not met, the statistic cannot be used.

The most recommendable is to apply the Central Limit Theorem, this theorem states:

Be a population with probability function f(X;μ,δ²) from which a random sample of size n is selected. Then the distribution of the sample mean tends to the normal distribution with mean μ and variance δ²/n when the sample size tends to infinity.

As a rule, a sample of size greater than or equal to 30 is considered sufficient to apply the theorem and use the approximation.

X[bar]≈N(μ; σ²/n)

Then you can use the standard normal approximation:

Z= X[bar] - μ ≈N(0;1)

σ/√n

The critical region for this test is one-tailed (left tail)

If , you reject the null hypothesis.

If -1.645" alt="Z_{H_0} > -1.645" align="absmiddle" class="latex-formula">, you do not reject the null hypothesis.

c)

The statistic is:

Z= -1.75

The p-value is one-tailed with the same direction of the test, you calculate it as:

P(Z < -1.75)= 0.04006

To decide using the p-value you have to compare it against the significance level.

If it is greater than the level of significance, then you don't reject the null hypothesis.

If it is equal or less than the level of significance, then you reject the null hypothesis.

d) The calculated p-value (0.04006) is less than α (0.05), the decision is to reject the null hypothesis.

e) At a level of 5%, the decision is to reject the null hypothesis. This means that there is significant evidence to think that the average level of arsenic in the well water is less than 8 ppb.

I hope it helps!

True or false: The mode is universally an accurate representation of data sets because it captures the number that occurs most often.

### Answers

Answer:

False

Step-by-step explanation:

Actually, the second side of the question is true. Yes, mode is the most frequent and often number captures the data set. But, it could not be said about the accurate and universal data sets representation. Because:

1) Sometimes mode might not be unique, it may have more than one so we will be stuck about choosing the best representation.

2) Or, if we have continuous data, we will have a lot of values so it will be tough to determine.

3) The problem of not being available to provide the very good measure of the central tendency. It happens, for instance, the mark mostly seen is very far from the rest of the data.