Stats 2510 - Exam 3

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A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of 100 doctors was chosen which resulted in 87 who indicate that they recommend this cough syrup. The test statistic in this problem is approximately:

-1

Find the value of the test statistic z. A claim is made that the proportion of children who play sports is less than 0.5, and the sample statistics include n = 1320 subjects with 30% saying that they play a sport.

-14.53

Use qt() to find the t-value, to two decimal places, for which the area below t is 0.005 with 14 degrees of freedom.

-2.98

Many samples of size n are selected at random from a population that has mean (mu) and a standard deviation (sigma). What of the following statements about the sampling distribution of the sample mean, x bar, is true?

-the mean of the sampling distribution of x bar is the same as the population mean -the variance of the sampling distribution of x bar is sigma^2/n -the standard deviation of the sampling distribution of x bar decreases as the sample size grows larger

Assume that the heights of men are normally distributed with a mean of 66.9 inches and a standard deviation of 2.1 inches. If 36 men are randomly selected, find the probability that they have a mean height greater than 67.9 inches.

0.0021

Assume that blood pressure readings are normally distributed with a mean of 117 and a standard deviation of 9.6. If 144 people are randomly selected, find the probability that their mean blood pressure will be less than 119.

0.0062

The business college computing center wants to determine the proportion of business students who have laptop computers. If the proportion differs from 30%, then the lab will modify a proposed enlargement of its facilities. Suppose a hypothesis test is conducted and the test statistic is 2.5. Find the p-value for a two-tailed test of hypothesis using pnorm().

0.0124

A one question survey is to be distributed to a random sample of 1500 adults in a particular state. The question asks if they support an increase in the state sales tax from 6% to 7%, with the additional revenue going to education. Let p^ denote the proportion of adults in the sample who say they support the increase. Suppose that 40% of all adults in this state support the increase. What is the standard deviation, σp^, of the sampling distribution of p^?

0.0126

Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis).The test statistic in a left-tailed test is z = -2.05.

0.0202; reject the null hypothesis

The average score of all golfers for a particular course has a mean of 70 and a standard deviation of 3.5. Suppose 49 golfers played the course today. Find the probability that the average score of the 49 golfers exceeded 71.

0.0228

Use pt() to find the probability, to three decimal places, that P(t>2.1) with 21 degrees of freedom.

0.024

A national caterer determined that 37% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If phat is the sample proportion saying that the food is delicious, what is the standard deviation of the sampling distribution of phat?

0.04

Use pt() to find the shaded area, to three decimal places, for a sample of size n = 18.

0.04

Use the given information and pnorm() to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With H1 : p > 0.554, the test statistic is z = 1.34.

0.0901; reject the null hypothesis

0.1032; fail to reject the null hypothesis

Use pt() to find P(t≤−1.2) , to three decimal places, using 15 degrees of freedom.

0.124

A greenhouse in a tri-county area has kept track of its customers for the last several years and has determined that 28% of its customers plant a vegetable garden in the spring. The greenhouse obtains a random sample of 1000 of its customers. What is the mean of the sampling distribution of phat, the sample proportion of customers that plant a vegetable garden in the spring?

0.28

0.3015; fail to reject the null hypothesis

A marketing research company is estimating which of two soft drinks college students prefer. A random sample of n college students produced the following 95% confidence interval for the proportion of college students who prefer drink A: (.262, .622). Identify the point estimate for estimating the true proportion of college students who prefer that drink.

0.442

A random sample of 4000 U.S. citizens yielded 2150 who are in favor of gun control legislation. Find the point estimate for estimating the proportion of all Americans who are in favor of gun control legislation.

0.5375

A random sample of 4000 U.S. citizens yielded 2250 who are in favor of gun control legislation. Estimate the true proportion of all Americans who are in favor of gun control legislation using a 90% confidence interval.

0.5625 +or- 0.0129

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the true proportion of students who receive financial aid.

0.59 +or- 0.004

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students and finds that 118 of them are receiving financial aid. Use a 95% confidence interval to estimate the true proportion of students who receive financial aid.

0.59 +or- 0.068

Professor Whata Guy surveyed a random sample of 420 statistics students. One of the questions was "Will you take another mathematics class?" The results showed that 252 of the students said yes. What is the sample proportion, of students who say they will take another math class?

0.6

To assess attitudes towards issues that affect the residents of a village, the village randomly chose 800 families to participate in a survey of life attitudes. The village received 628 completed surveys. What is the sample proportion of completed surveys?

0.785

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 20.6 and standard deviation of 5.2. At Northside High School, 36 seniors take the test. What is the standard deviation of the sampling distribution of X¯ for random samples of 36 students? Round your answer to three decimal places.

0.867

A national caterer determined that 87% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. If phat is the sample proportion saying that the food is delicious, what is the mean of the sampling distribution of phat?

0.87

The scores of individual students on the American College Testing Program Composite College Entrance Examination have a normal distribution with mean = 18.6 and standard deviation = 6. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?

Suppose a population has a mean of 7 for some characteristic of interest and a standard deviation of 9.6. A sample is drawn from this population of size 64. What is the standard error of the mean?

1.2

Based on past experience, a bank believes that 6% of the people who receive loans will not make payments on time. The bank has recently approved 300 loans. What is the standard deviation of the proportion of clients in this group who may not make timely payments?

1.37%

The director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a period. The director randomly selects 49 different periods and determines the number of admissions for each. For this sample, and Estimate the mean number of admissions per period with a 95% confidence interval.

15.3 +or- 1.4

A random sample of 250 students at a university finds that these students take a mean of 15.8 credit hours per quarter with a standard deviation of 2.3 credit hours. Estimate the mean credit hours taken by a student each quarter using a 90% confidence interval. Round to the nearest thousandth

15.8 +or- 0.239

The scores of individual students on the American College Testing Program Composite College Entrance Examination have a normal distribution with mean = 18.6 and standard deviation = 6. At Northside High, 36 seniors take the test. Assume the scores at this school have the same distribution as national scores. What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?

18.6

Find the confidence interval specified. Assume that the population is normally distributed.A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 206 milligrams with s = 12.7 milligrams. Construct a 95% confidence interval for the true mean cholesterol content of all such eggs.

197.9 to 214.1 milligrams

Suppose a population has a mean weight of 180 pounds and a standard deviation of 25 pounds. A sample of 100 items is drawn from this population. What is the standard error of the mean?

2.5

A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.5%, 4.2%). What is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?

2.85%

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 20.6 and standard deviation of 5.2. At Northside High School, 36 seniors take the test. What is the mean of the sampling distribution of X¯ for random samples of 36 students?

20.6

In a sample of size 25, in order to compute any sample statistic, how many sample values are free to vary?

40%

Find the confidence interval specified. Assume that the population is normally distributed.A sociologist develops a test to measure attitudes about public transportation, and 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.

67.7 to 84.7

How much money does the average professional football fan spend on food at a single football game? That question was posed to 60 randomly selected football fans. The sampled results show that the sample mean was $70.00 and prior sampling indicated that the population standard deviation was $17.50. Use this information to create a 95 percent confidence interval for the population mean.

70 +or- 1.960(17.50/sqrt(60))

Suppose a large labor union wishes to estimate the mean number of hours per month a union member is absent from work. The union decides to sample 426 of its members at random and monitor the working time of each of them for 1 month. At the end of the month, the total number of hours absent from work is recorded for each employee. If the mean and standard deviation of the sample are x=9.5 hours and s=2.2 hours, find a 99% confidence interval for the true mean number of hours a union member is absent per month. Round to the nearest thousandth.

9.5 +or- 0.274

A random sample of n measurements was selected from a population with unknown mean μ and known standard deviation σ. Calculate a 95% confidence interval for μ for the given situation. Round to the nearest hundredth when necessary.n = 125, = 91, σ = 20

91 +or- 3.51

An SRS of 100 postal employees found that the average amount of time these employees had worked forthe U.S. Postal Service was x¯ = 7 years, with a standard deviation of s = 2 years. Assume thedistribution of the time the population of all postal employees has worked for the Postal Service isapproximately normal with mean 𝜇. Do the observed data represent evidence that 𝜇 has changed fromits value of 7.5 years of 20 years ago? To determine this, we test the hypotheses H0: 𝜇 = 7.5, Ha: 𝜇 ≠ 7.5using the one-sample t test. How many degrees of freedom should be considered for this test?

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, p, σ) for the indicated parameter.An entomologist writes an article in a scientific journal which claims that fewer than 16 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

H0 : p = 0.0016 H1 : p < 0.0016

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ, p, σ) for the indicated parameter. A psychologist claims that more than 5.8 percent of the population suffers from professional problems due to extreme shyness. Use p, the true percentage of the population that suffers from extreme shyness.

H0 : p = 5.8% H1 : p > 5.8%

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the association's name. The association's by-laws require that more than 60 percent of the association must approve a name change. Rather than convene a meeting, it is first desired to use a sample to determine if meeting is necessary. Identify the null and alternative hypothesis that should be tested to determine if a name change is warranted.

H0: p > 0.6, Ha: p < 0.6

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 68 tissues during a cold. Suppose a random sample of 2500 people yielded the following data on the number of tissues used during a cold: = 55, s = 23. Identify the null and alternative hypothesis for a test to determine if the mean number of tissues used during a cold is less than 68.

H0: μ = 68, Ha: μ < 68

A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.3 hours. In order to test whether the time to fill out the form has been reduced, a sample of 48 small business owners who annually complete the form was randomly chosen, and their completion times recorded. The mean completion time for ABC-5500 form was 5.7 hours with a standard deviation of 1.8 hours. In order to test that the time to complete the form has been reduced, state the appropriate null and alternative hypotheses.

H0: μ > 6.3, Ha: μ < 6.3

The weights of extra-large eggs have a normal distribution with a mean of 1oz and a standard deviation of 0.1oz. What is the sampling distribution of the sample mean weight of the eggs in a randomly selected carton of a dozen eggs?

N(1, 0.029)

The weights of medium oranges packaged by an orchard are normally distributed with a mean of 14oz and a standard deviation of 2oz. Ten medium oranges will be randomly selected from a package. What is the sampling distribution of the sampling mean weight of a random sample of ten medium oranges?

N(14, 0.63)

A company claims that 9 out of 10 doctors (i.e., 90%) recommend its brand of cough syrup to their patients. To test this claim against the alternative that the actual proportion is less than 90%, a random sample of doctors was taken. Suppose the test statistic is z = -1.75. Can we conclude that H0 should be rejected at the a) a=0.1 b)a=0.05 and c) a=0.01 level?

a) yes b) yes c) no

The mean annual income for adult women in one city is $28,520 and the standard deviation of the incomes in $5100. The distribution of incomes is skewed to the right. Determine the sampling distribution of the mean for samples of size 74.

approximately normal mean $28,520, standard deviation =$593

The number of violent crimes committed in a day possesses a distribution with a mean of 3.5 crimes per day and a standard deviation of 4 crimes per day. A random sample of 100 days was observed, and the mean number of crimes for the sample was calculated. Describe the sampling distribution of the sample mean.

approximately normal with mean = 3.5 and standard deviation = 0.4

For the population of one town, the number of siblings, x, is a random variable whose relative frequency histogram has a reverse J shape. The mean number of siblings is 1.3 and the standard deviation is 1.5. Let x bar denote the mean number of siblings for a random sample of size 31. Determine the sampling distribution of the mean for samples of size 31.

approximately normal, mean = 1.3, standard deviation = 0.27

Which of the following statements is false regarding the t-distribution?

as the degrees of freedom get smaller, the t-distribution's spread gets smaller

A national organization has been working with utilities throughout the nation to find sites for large wind machines that generate electricity. Wind speeds must average more than 25 miles per hour (mph) for a site to be acceptable. Recently, the organization conducted wind speed tests at a particular site. Based on a sample of n=43 wind speed recordings (taken at random intervals), the wind speed at the site averaged x=25.8mph, with a standard deviation of s=4.2mph. To determine whether the site meets the organization's requirements, consider the test, H0: μ = 25, Ha: μ ≠ 25 where μ is the true mean wind speed at the site and a=0.01. Suppose the value of the test statistic were computed to be 1.25. State the conclusion.

at a=0.01, there is insufficient evidence to conclude the true mean wind speed at the site exceeds 25 mph

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 54 tissues during a cold. Suppose a random sample of 100 people yielded the following data on the number of tissues used during a cold: x=46, s=20 Suppose the corresponding test statistic falls in the rejection region at a=0.05. What is the correct conclusion?

at a=0.05, reject H0

A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 64 bottles and finds the average amount of liquid held by the bottles is 11.9155 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is 0.0455. State the proper conclusion.

at a=0.05, reject the null hypothesis

A small private college is interested in determining the percentage of its students who live off campus and drive to class. Specifically, it was desired to determine if less than 20% of their current students live off campus and drive to class. A sample of 108 students was randomly selected and the following printout was obtained: Hypothesis Test - One Proportion Sample Size 108 Successes 16 Proportion 0.14815 Null Hypothesis: P = 0.2 Alternative Hyp: P < 0.2 Difference -0.05185 Standard Error 0.03418 Z -1.35 p-value 0.0885 Based on the information contained in the printout, what conclusion would be correct when testing at a=0.05.

fail to reject H0

Given H0: μ = 18, Ha: μ < 18, and p = 0.068. Do you reject or fail to reject H0 at the .05 level of significance?

fail to reject H0

Given H0: μ = 25, Ha: μ ≠ 25, and p = 0.033. Do you reject or fail to reject H0 at the .01 level of significance?

fail to reject H0

The owner of a football team claims that the mean attendance at games is over 59,100, and he is therefore justified in moving the team to a city with a larger stadium. Identify the type II error for the test.

fail to reject the claim that the mean attendance is equal to 59,100, when it is actually greater than 59,100

T/F A 95% confidence interval for a mean indicates that the probability that the population mean is in the interval is 0.95.

false

T/F The sampling distribution of the sample proportion can be considered normal if the sample observations are independent and there are at least 30 expected successes and 30 expected failures in the sample.

false

T/F Without using RStudio, determine whether the following statement is true or false. The P(t<−2), using 12 degrees of freedom is less than 0.025.

false

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for μ.

in repeated sampling, 95% of similarly constructed intervals contain the value of the population mean

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($100,951, $115,349) To make more useful inferences from the data, it is desired to reduce the width of the confidence interval. Which of the following will result in a reduced interval width?

increase the sample size and increase the confidence level

For the given binomial sample size and null-hypothesized value of p0, determine whether the sample size is large enough to use the normal approximation methodology to conduct a test of the null hypothesis H0:p=p0 n = 800, p0 = 0.99

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 90% confidence interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .460 LOWER LIMIT = .332 Based on the interval above, do you believe that 31% of all college students prefer American automobiles?

no and we are 90% confident of it

The amount of money collected by a snack bar at a large university has been recorded daily for the past five years. Records indicate that the mean daily amount collected is $3650 and the standard deviation is $600. The distribution is skewed to the right due to several high volume days. Suppose that 100 days were randomly selected from the five years and the average amount collected from those days was recorded. Which of the following describes the sampling distribution of the sample mean?

normally distributed with a mean of $3650 and a standard deviation of $60

The registrar's office at State University would like to determine a 95% confidence interval for the mean commute time of its students. A member of the staff randomly chooses a parking lot and surveys the first 200 students who park in the chosen lot on a given day. The confidence interval is

not meaningful because of the lack of random sampling

A Type I error is the mistake of ________ when it is actually true.

rejecting the null hypothesis

Suppose we want to test the claim that the majority of adults are in favor of a national health insurance system. Is the hypothesis test left-tailed, right-tailed, or two-tailed?

right tailed

according to the law of large numbers, as more observations are added to the sample, the difference between the sample mean and the population mean

tends to become smaller

A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the P-value approach. Also, assess the strength of the evidence against the null hypothesis. x = 24.4, s=9.2, n = 25, H0: μ = 26, Ha: μ < 26, a=0.05. Use the Empirical Rule, not R, to help you draw the conclusion of the test.

test statistic t=-0.87. p-value > 0.16. do not reject H0. There is not sufficient evidence to conclude that the mean is different from 26. The evidence against the null hypothesis is weak or none

A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the P-value approach. Also, assess the strength of the evidence against the null hypothesis. overbar(x) = 137, s = 14.2, n = 20, H0: μ = 132, Ha: μ ≠ 132, α = 0.1

test statistic t=1.57. p-value-0.1318. do not reject H0. There is not sufficient evidence to conclude that the mean is different from 132. The evidence against the null hypothesis is weak or none

A sample mean, sample standard deviation, and sample size are given. Use the one-mean t-test to perform the required hypothesis test about the mean, μ, of the population from which the sample was drawn. Use the P-value approach. Also, assess the strength of the evidence against the null hypothesis. x = 226,450, s =11,500, n = 23, H0: μ = 220,000, Ha: μ > 220,000, a=0.01

test statistic t=2.69. p-value=0.00669. reject the null hypothesis. There is sufficient evidence to conclude that the mean is different from 220,000. The evidence against the null hypothesis is very strong

Use the given information and the Empirical Rule to estimate the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z = 0.52.

the p-value is greater than 0.16; fail to reject the null hypothesis

Use the given information to and the Empirical Rule to estimate the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). With Ha : p > 0.554, the test statistic is z = 2.34.

the p-value is less than 0.025; reject the null hypothesis

The scores of individual students on the American College Testing (ACT) Program Composite College Entrance Examination have a Normal distribution with mean 20.6 and standard deviation of 5.2. At Northside High School, 36 seniors take the test. How will the standard deviation of the sampling distribution of X¯ for random samples of 36 students compare to the standard deviation of the population distribution of scores?

the standard deviation of the sampling distribution will be smaller than the standard deviation of the population distribution of the scores

The owner of a football team claims that the average attendance at games is over 523, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test to support this claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

there is not sufficient evidence to support the claim that the mean attendance is greater than 523

Carter Motor Company claims that its new sedan, the Libra, will average better than 32 miles per gallon in the city. Assuming that a hypothesis test to support this claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

there is sufficient evidence to support the claim that the mean is greater than 32 miles per gallon

T/F A confidence interval gives a plausible range of values for a population parameter.

true

T/F A sample proportion can be thought of as a sample mean because we calculation the proportion as the total number of successes divided by the total number of trials.

true

T/F The margin of error represents the distance from the point estimate to the lower and upper bounds of a confidence interval.

true

T/F Without using RStudio, determine if the following statement is true or false. The P(t>3.4) is less than 0.05.

true

We use the sample proportion, p^, as a point estimator for the population proportion, p

true

When the conditions are met for the sampling distribution of the sample proportion to be considered normal, the mean of the sampling distribution will be equivalent to the population proportion p with a standard error of sqrt(p(1−p)/n)

true

A 90% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($146,132, $156,381) Give a practical interpretation of the interval.

we are 90% confident that the mean salary of all CEOs in the electronics industry falls in the interval $146,132 to $156,381

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below of a 99% confidence interval for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396 SAMPLE SIZE = 159 UPPER LIMIT = .496 LOWER LIMIT = .296 Which of the following is a correct practical interpretation of the interval?

we are 99% confident that the proportion of all college students who prefer american cars falls between 0.296 and 0.496

When estimating the population mean μ with a confidence interval, what value is at the center of the confidence interval?

x bar

A greenhouse in a tri-county area has kept track of its customers for the last several years and has determined that it has about 10,000 regular customers. Of those customers, 28% of them plant a vegetable garden in the spring. The greenhouse obtains a random sample of 800 of its customers. Is it safe to assume that the sampling distribution of phat, the sample proportion of customers that plant a vegetable garden, is approximately normal? Answer Yes or No.

yes

A national caterer determined that 87% of the people who sampled their food said that it was delicious. A random sample of 144 people is obtained from a population of 5000. The 144 people are asked to sample the caterer's food. Will the distribution of phat, the sample proportion saying that the food is delicious, be approximately normal? Answer Yes or No.

yes

yes, since both np and nq are greater than or equal to 10

What type of car is more popular among college students, American or foreign? One hundred fifty-nine college students were randomly sampled and each was asked which type of car he or she prefers. A computer package was used to generate the printout below for the proportion of college students who prefer American automobiles. SAMPLE PROPORTION = .396226 SAMPLE SIZE = 159 UPPER LIMIT = .46353 LOWER LIMIT = .331114 Is the sample large enough for the interval to be valid?

yes, since expected successes and expected failures are both greater than 10

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2 and 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test.

z=0.173

Researchers are concerned that the mean clutch size (number of eggs per nest) of robin's eggs in a particular forest has decreased from the mean of 4.8 eggs measured 10 years ago. They send out teams to locate and count the number of eggs in 200 different nests in randomly selected areas and find the mean to be 4.75 with a standard deviation of 1.4 . Find the value of the test statistic to perform this test.

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