stat exam 3

A Type I error is committed when

you reject a null hypothesis that is true

True or False: When the sample sizes are equal, the pooled variance of the two groups is the average of the 2 sample variances.

true

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000

two-tail

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5, 95.4, and 220.0. Summary statistics yield = 180.975 and S = 143.042. Calculate a 95% confidence interval for the mean endowment of all the private colleges in the United States assuming a normal distribution for the endowments.

$180.975 ± $115.586

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below.​AmericanJapaneseSample Size211100Sample Mean SSATL Score65.7579.83Sample Std. Dev.11.076.41Referring to Scenario 10-1, what is the value of the test statistic?

-11.8092

A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim against the alternative that the actual proportion of doctors who recommend aspirin is less than 0.90, a random sample of 100 doctors results in 83 who indicate that they recommend aspirin. The value of the test statistic in this problem is approximately equal to:

-2.33

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She would now like to determine whether or not the mean age of her customers is greater than 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 30.45 years and the sample standard deviation was 5 years. What is the p-value associated with the test statistic?

.0780

When testing H0 : π1 — π2 ≤ 0 versus H1 : π1 — π2 > 0, the observed value of the Z test statistic was found to be — 2.13. The p-value for this test is

.9834

An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What is the upper end in a 99% confidence interval for the average income?

15364

An economist is interested in studying the incomes of consumers in a country. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in a mean income of $15,000. What total sample size would the economist need to use for a 95% confidence interval if the width of the interval should not be more than $100?

1537

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. If the dean wanted to estimate the proportion of all students receiving financial aid to within 3% with 99% reliability, how many students would need to be sampled?

1784

The Wall Street Journal recently ran an article indicating differences in perception of sexual harassment on the job between men and women. The article claimed that women perceived the problem to be much more prevalent than did men. One question asked to both men and women was: "Do you think sexual harassment is a major problem in the American workplace?" Some 24% of the men compared to 62% of the women responded "Yes." Suppose that 150 women and 200 men were interviewed. For a 0.01 level of significance, what is the critical value for the rejection region?

2.33

If you were constructing a 99% confidence interval of the population mean based on a sample of n = 25 where the standard deviation of the sample S = 0.05, the critical value of t will be

2.7969

The head librarian at the Library of Congress has asked her assistant for an interval estimate of the mean number of books checked out each day. The assistant provides the following interval estimate: from 740 to 920 books per day. What is an efficient, unbiased point estimate of the number of books checked out each day at the Library of Congress?

830

You know that the probability of committing a Type II error (β) is 5%, you can tell that the power of the test is

95

Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. The proper conclusion for this test is:

At the α = 0.10 level, there is sufficient evidence to indicate that females have a lower mean starting salary than male MBA graduates.

Which of the following would be an appropriate null hypothesis?

The mean of a population is equal to 55.

In testing for differences between the means of two independent populations, the null hypothesis is:

H0 : μ1 — μ2 = 0.

Referring to Scenario 10-2, the researcher was attempting to show statistically that the female MBA graduates have a significantly lower mean starting salary than the male MBA graduates. Which of the following is an appropriate alternative hypothesis?

H1: μfemales < μmales

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered the Sarnoff Survey of Attitudes Toward Life (SSATL), which measures motivation for upward mobility. The SSATL scores are summarized below. ​AmericanJapaneseSample Size211100Sample Mean SSATL Score65.7579.83Sample Std. Dev.11.076.41 Referring to Scenario 10-1, judging from the way the data were collected, which test would likely be most appropriate to employ?

Pooled-variance t test for the difference between two means

You have created a 95% confidence interval for μ with the result 10 ≤ μ ≤ 15. What decision will you make if you test H0 : μ = 16 versus H1 : μ ≠ 16 at α = 0.05?

Reject H0 in favor of H1.

A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.

The null hypothesis is rejected.

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, what can you conclude?

There is not enough evidence to conclude that the daily mean revenue was not $675.

It is desired to estimate the mean total compensation of CEOs in the Service industry. Data were randomly collected from 18 CEOs and the 95% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

We are 95% confident that the mean total compensation of all CEOs in the Service industry falls in the interval $2,181,260 to $5,836,180.

A 99% confidence interval estimate can be interpreted to mean that

both above

Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). 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 same size

How many tissues should the Kimberly Clark Corporation package of Kleenex contain? Researchers determined that 60 tissues is the mean number of tissues used during a cold. Suppose a random sample of 100 Kleenex users yielded the following data on the number of tissues used during a cold: = 52, S = 22. Using the sample information provided, calculate the value of the test statistic.

t = (52 - 60) / (22/10)

A real estate company is interested in testing whether the mean time that families in Gotham have been living in their current homes is less than families in Metropolis. Assume that the two population variances are equal. A random sample of 100 families from Gotham and a random sample of 150 families in Metropolis yield the following data on length of residence in current homes.Gotham: G = 35 months, SG2 = 900 Metropolis: M = 50 months, SM2 = 1050Referring to Scenario 10-3, what is(are) the critical value(s) of the relevant hypothesis test if the level of significance is 0.05?

t ≅ Z = — 1.645

A ________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

test statistic

True or False: The sample mean is a point estimate of the population mean.

true