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A Type I error is committed when

you reject a null hypothesis that is true.

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?

$15,365

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. What value will be used as the point estimate for the mean endowment of all private colleges in the United States?

$180.975

Assume we do not know the population standard deviation of amount spent. But, in the 15 credit card accounts, the sample standard deviation (S) is $20. The mean amount spent in the sample was found to be $50.50. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall.

$39.42, $61.58

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were randomly sampled and the mean was found to be $50.50. You may assume the amount spent in the population has a normal distribution. Assume the population standard deviation of amount spent is known to be $20. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall.

$40.38, $60.62

Assume we do not know the population standard deviation of amount spent. But, in 25 credit card accounts, the sample standard deviation (S) is $20. (Note sample size increased from 15 to 25.) The mean amount spent in the sample was found to be $50.50. Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store in the mall.

$42.24, $58.76

An advertisement claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. A random sample of 100 doctors results in 83 who indicate that they recommend aspirin. You wish to conduct a hypothesis test that the true proportion is less than or equal to 0.90. The value of the test statistic for your hypothesis test is:

- 2.33

A researcher randomly sampled 30 graduates of an MBA program and recorded data concerning their starting salaries. Of primary interest to the researcher was the effect of gender on starting salaries.Tabulations from the sample are given below. What is the 95% confidence interval estimate for the difference between two means (female minus male)? HINT: Sp2=166,073,417. Use t-table with 28 degrees of freedom to find critical values. second graph

-$16,455 to $3,235

Suppose you wish to test whether the mean Attitudes score of American managers differs from the mean score of Japanese managers (mean score for American managers minus mean score for Japanese managers). What is the value of your test statistic? HINT: Sp2=96.447 same graph

-11.8

Suppose a bank examines a sample of 31 checking accounts and finds the mean balance is $3,500. The standard deviation for balances in all accounts is not known but the sample standard deviation is $500. Suppose the bank manager wants to test the null hypothesis that mean balance in all checking accounts is $3,600 against an alternative that mean balance is different than $3,600. What are the critical values for an =0.05 level test?

-2.042, 2.042

If you wish to conduct a hypothesis test about whether proportions for each group are the same or not, what is your p-value? HINT: Use the standard normal lookup table to find the probability of getting a z-value less than the test statistic you found in question 11. Subtract the probability from 1 as part of your calculations. 3rd

0.017 x 2

What is the 90% confidence interval estimate of the difference between the proportion of males and females who prefer Pepsi? HINT: Critical value for a 90% confidence interval is +/- 1.645. Use p1, p2, sample sizes and formula from lecture. 3rd

0.05 to 0.30

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She knows the standard deviation of age is equal to 5. She would like to determine whether or not the mean age of her customers is 30. Suppose she found that the sample mean was 30.45 years. What is the p-value for the hypothesis test?

0.16 test statistic is (30.45-30) / (5/sqrt(250)) = 1.42. Probability of getting 1.42 or higher is 0.0778. 2 times this value is the p-value: 0.1556 or about 0.16

Democrats hold a one-point advantage over Republicans in a generic congressional ballot just weeks out from the midterm elections, according to an NBC News poll released Sunday. ◼ About 47 percent of Americans back a Democrat controlled Congress while 46 percent say they would like to see a Republican-controlled Congress, the poll shows. ◼ The NBC News poll was conducted from Oct. 14 to Oct. 18 among 1,000 registered voters by Hart Research Associates. What is a 95 percent confidence interval for the percentage of registered voters in the United States who favor a Democrat-controlled Congress?

0.439, 0.501

A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no". A 99% confidence interval for the proportion of the student population who feel comfortable reporting cheating by their fellow students is from __________ to __________:

0.456 to 0.504

A sales and marketing management magazine conducted a survey on salespeople cheating on their expense reports and other unethical conduct. In the survey on 200 managers, 58% of the managers have caught salespeople cheating on an expense report. What is the 95% confidence interval estimate of the population proportion of managers who have caught salespeople cheating on an expense report?

0.51 to 0.65

Suppose the alternative hypothesis is the business school preparation course is effective in improving exam scores. What is the critical value for testing at the 5% level of significance? HINT: Use t-table and note this is a one-tail test. 5th

1.895

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. What is the critical value used in constructing a 90% confidence interval?

1.895

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12.00 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. The confidence interval goes from ________ to ________.

12.09 to 12.19

If you wish to conduct a hypothesis test about whether proportions for each group are the same or not, what is your test statistic? HINT: First calculate , the pooled estimate of the overall proportion, and use in formula from lecture. 3rd graph

2.12

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12.00 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. The critical value to use in obtaining the confidence interval is

2.58

The use of preservatives by food processors has become a controversial issue. Suppose two preservatives are extensively tested and determined safe for use in meats. A processor wants to compare the preservatives for their effects on retarding spoilage. Suppose 15 cuts of fresh meat are treated with preservative I and 15 are treated with preservative II, and the number of hours until spoilage begins is recorded for each of the 30 cuts of meat. The results are summarized in the table below. What is the value of the test statistic for testing if the population variances differ for preservatives I and II? 4th

2.64

True or false: The confidence interval you calculated in question # 2 suggests that the machine is not working properly.

False

If we are testing for the difference between the means of 2 independent populations presuming equal variances with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to

38

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. A 90% confidence interval for the mean score of actuarial students in the special program is

4.66 to 7.34

Given the following information, calculate Sp2, the pooled sample variance that should be used in the pooled-variance t test. S12 = 4 S22 = 6 n1 = 16 n2 = 25

5.23

What is the value of the sample mean difference if the difference scores reflect the results of the exam after the course minus the results of the exam before the course? HINT: Copy the table into Excel to do the calculations. 5th

50

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. The mean of the sample and standard deviation of the sample, respectively, are:

6.0, 2.0

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. The confidence interval will be based on how many degrees of freedom?

7

When you test for differences between the means of two independent populations, you can only use a two-tail test.

False

The t-distribution is especially important when analyzing

A mean from a very small sample

If you wish to conduct a hypothesis test about whether proportions for each group are the same or not at the 0.01 level of significance, what is your conclusion? HINT: the critical values for the 0.01 two tail test are +/- 2.58 3rd graph

Do not reject the hypothesis of equal proportions

Suppose a bank examines a sample of 31 checking accounts and finds the mean balance is $3,500. The standard deviation for balances in all accounts is not known but the sample standard deviation is $500. Suppose the bank manager wants to test the null hypothesis that mean balance in all checking accounts is $3,600 against an alternative that mean balance is different than $3,600. Using a significance level of 0.05, what would you conclude?

Do not reject the null hypothesis Without population standard deviation, no conclusion can be reached

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She knows the standard deviation of age is equal to 5. She would now like to determine whether or not the mean age of her customers is 30. Suppose she found that the sample mean was 30.45 years. If she wants to have a level of significance at 0.01 what conclusion can she make?

Do not reject the null hypothesis that mean age is 30

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. True or False: If the same sample had been used to test the null hypothesis that the mean of the population is equal to 18 versus the alternative hypothesis that the mean of the population differs from 18, the null hypothesis could be rejected at a level of significance of 0.05.

False

A statistics professor wanted to test whether the grades on a statistics test were the same for upper and lower classmen. The professor took a random sample of size 10 from each and conducted a test and found out that the variances were equal. For this situation, the professor should use a paired t test for related samples.

False

A university wanted to find out the percentage of students who felt comfortable reporting cheating by their fellow students. A survey of 2,800 students was conducted and the students were asked if they felt comfortable reporting cheating by their fellow students. The results were 1,344 answered "Yes" and 1,456 answered "no". True or False: The parameter of interest is the total number of students in the population who feel comfortable reporting cheating by their fellow students.

False

Holding the level of confidence fixed, increasing the sample size will lead to a wider confidence interval

False

In a hypothesis test, it is irrelevant whether the test is a one-tail or two-tail test.

False

Suppose, in testing a hypothesis about a mean, the Z test statistic is computed to be 2.04. The null hypothesis should be rejected if the chosen level of significance is 0.01 and a two-tail test is used.

False

The larger the p-value, the more likely you are to reject the null hypothesis.

False

The t-distribution is used for confidence intervals for means when the population standard deviation is known.

False

The t-distribution is used in determining confidence intervals for proportions.

False

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired mean length of the insulation is 12.00 feet. It is known that the standard deviation in the cutting length is 0.15 feet. A sample of 70 cut sheets yields a mean length of 12.14 feet. This sample will be used to obtain a 99% confidence interval for the mean length cut by machine. In the above scenario, the confidence interval is valid only if the lengths cut by the machine are normally distributed.

False Normality is not required because n > 30 and sampling distribution of means would be normal.

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She knows the standard deviation of age is equal to 5. She would like to determine whether or not the mean age of her customers is is 30. The appropriate hypotheses to test are:

H0: =30 H1: =/30

Are Japanese managers more motivated than American managers? A randomly selected group of each were administered an Attitudes test, which measures motivation for upward mobility. Researchers were interested in whether mean scores are different. The Attitudes scores are summarized below. Which test would likely be most appropriate to employ? graph on phone

Pooled-variance t test for the difference between two means

The owner of a local nightclub has recently surveyed a random sample of n = 250 customers of the club. She knows the standard deviation of age is equal to 5. She would like to determine whether or not the mean age of her customers is is 30. If she wants to have a level of significance at 0.01, what rejection region should she use?

Reject H0 if z < -2.58 or z > 2.58 Reject H0 if z < - 1.645.

Suppose you wish to test whether the mean Attitudes score of American managers differs from the mean score of Japanese managers (mean score for American managers minus mean score for Japanese managers). All of the multiple choice responses in the prior question suggest the test statistic is an extreme negative number and the sample sizes for each group are reasonably large. What is the p-value associated with the hypothesis test? same graph

Smaller than 0.01

Which of the following represents the result of a hypothesis test that variances are equal or not at the 0.10 signifcance level? HINT: Use excel =F.INV.RT(0.05,14,14) to get critical value 4th

The null hypothesis is rejected.

What assumptions were necessary to conduct a pooled-variance hypothesis test? HINT: See Section 10.1 in textbook. second graph

The population variances are approximately equal. Both populations of salaries (male and female) must have approximate normal distributions. The population variances are approximately equal. The samples were randomly and independently selected.

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 was selected. Suppose you reject the null hypothesis. What conclusion can you reach?

There is sufficient evidence that the proportion of doctors who recommend aspirin is less than 0.90

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 15 to 19. True or False: If the same sample had been used to test the null hypothesis that the mean of the population is equal to 20 versus the alternative hypothesis that the mean of the population differs from 20, the null hypothesis could be rejected at a level of significance of 0.05.

True

If the p-value is low, the null hypothesis must go.

True

Suppose, in testing a hypothesis about a mean, the p-value is computed to be 0.043. True or False: The null hypothesis should be rejected if the chosen level of significance is 0.05.

True

We do not say we accept the null

True

We reject or do not reject the null

True

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

True

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. True or False: For the confidence interval to be valid, it is necessary that population test scores of students in the special study program on the actuarial exam be normally distributed.

True True. n < 30, so assumption of normality in the population is necessary

To become an actuary, it is necessary to pass a series of 10 exams, including the most important one, an exam in probability and statistics. An insurance company wants to estimate the mean score on this exam for actuarial students who have enrolled in a special study program. They take a sample of 8 actuarial students in this program and determine that their scores are: 2, 5, 8, 8, 7, 6, 5, and 7. This sample will be used to calculate a 90% confidence interval for the mean score for actuarial students in the special study program. True or False: It is possible that the confidence interval obtained will not contain the mean score for all actuarial students in the special study program.

True We can only be 90 percent confident, not certain, true value will be in confidence interval.

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

a one-tail test should be utilized

An advertisement claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. Suppose the null hypothesis is the true proportion is greater than or equal to 0.9 and the alternative is that the true proportion is less than 0.9. A random sample of 100 doctors results in 83 who indicate that they recommend aspirin. Can you conclude that H0 should be rejected at the (a) = 0.10, (b) = 0.05, and (c) = 0.001 significance level?

a) yes; (b) yes; (c) no

The width of a confidence interval estimate for a proportion will be

narrower for 90% confidence than for 95% confidence

Suppose the alternative hypothesis is the business school preparation course is effective in improving exam scores. At the 0.05 level of signifcance, the decision would be? HINT: Copy table into excel and use =STDEV.S() function to get sample standard deviation. Then use that and other information to compute a test statistic. 5th

reject the null hypothesis in favor of the alternative

The power of a test is measured by its capability of

rejecting a null hypothesis that is false.

A Type II error is committed when

you don't reject a null hypothesis that is false.

If the p-value is less than (the level of signficance) in a two-tail test,

the null hypothesis should be rejected.