Stats FINAL

compute the p-value assuming that the hypothesis test is a one-tailed test: z = -1.55.

0.0606

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles how large could the sample mean be before they would reject the null hypothesis?

16.041 ounces

A large Midwestern university is interested in estimating the mean time that students spend at the student recreation center per week. A previous study indicated that the standard deviation in time is about 40 minutes per week. If the officials wish to estimate the mean time within ± 10 minutes with a 90 percent confidence, what should the sample size be?

44

Referring to Table 9-1, state the alternative hypothesis for this study.

H1: > 20.000

An analyst plans to test whether the standard deviation for the time it takes bank tellers to provide service to customers exceeds the standard of 1.5 minutes. The correct null and alternative hypothesis for this test are:

Ho: σ2 ≤ 2.25 Ha: σ2 > 2.25

For a one-tailed test (lower tail), a sample size of 10 at 90% confidence, t=

-1.383

For a one-tailed test (upper tail) at 93.7% confidence, Z =

1.53

referring to table 9-3 the value of the test statistic is

2.18

True or False: A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 time is 4.52 seconds to 5.18 seconds.

False

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. If the head librarian knows that the population standard deviation is 150 books checked out per day, approximately how large a sample did her assistant do

It cannot be determined from the information given.

Suppose we want to test Ho:(mew) = 30 Ha: <0 Which of the following possible sample results based on a sample of size 36 gives the strongest evidence to reject H0 in favor of Ha?

X= 27, s = 4

Referring to table 9-3, for a test with a significance level of 0.05, the critical value would be

z= 1.645

When the following hypotheses are being tested at a level of significance of α H0: μ <= 100 Ha: μ < 100 the null hypothesis will be rejected if the p-value is

α

When testing a two-tailed hypothesis using a significance level of 0.05, a sample size of n = 16, and with the population standard deviation unknown, which of the following is true?

All of the above are true

If a hypothesis test for a single population variance is to be conducted, which of the following statements is true

All of the following statements are true

If a manager believes that the required sample size is too large for a situation in which she desires to estimate the mean income of blue collar workers in a state, which of the following would lead to a reduction in sample size?

All options are correct

Read the Z statistic from the normal distribution table and circle the correct answer. A one-tailed test (upper tail) at 87.7% confidence; Z =

1.16

In order to test the following hypotheses at an α level of significance H0: μ <= 100 Ha: μ > 100 the null hypothesis will be rejected if the test statistic Z is

> = Zα

The managers of a local golf course have recently conducted a study of the types of golf balls used by golfers based on handicap. A joint frequency table for the 100 golfers covered in the survey is show below: If a player comes to the course using a Nike golf ball, the probability that he or she has a handicap of at least 10 is:

0.455.

For a one-tailed test (upper tail), a sample size of 18 at 95% confidence, t=

1.740

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The p-value associated with the test statistic in this problem is approximately equal to:

0.0026

referring to table 9-3, the p-value of the test is

0.0148

Compute the p-value assuming that the hypothesis test is a one-tailed test: z = 1.34

0.0901

It is desired to estimate the average 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). Based on the interval above, do you believe the average total compensation of CEOs in the Service industry is more than $3,000,000?

I cannot conclude that the average exceeds $3,000,000 at the 97% confidence level

In testing the hypothesis H0: μ = 100 vs. H1: μ > 100, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true?

The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074

data was randomly collected from 18 CEOs and the 97% confidence interval was calculated to be ($2,181,260, $5,836,180). Which of the following interpretations is correct?

We are 97% confident that the average total compensation of all CEOs in the service falls in the interval $2,181,260 to $5,836,180

A hypothesis test is to be conducted using an alpha = .05 level. This means:

there is a maximum 5 percent chance that a true null hypothesis will be rejected.

The p-value

is a probability

If a hypothesis is rejected at the 5% level of significance, it

may be rejected or not rejected at the 1% level

If the level of significance of a hypothesis test is raised from .01 to .05, the probability of a Type II error

will decrease

For a one-tailed hypothesis test (upper tail) the p-value is computed to be 0.034. If the test is being conducted at 95% confidence, the null hypothesis

is rejected

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that p is estimated to be, the __________ the sample size required.

larger

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average 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: X = 52, s = 22. Using the sample information provided, calculate the value of the test statistic.

-3.634

An assumption made about the value of a population parameter is called a

Hypothesis

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 within 3% with 99% reliability, how many students would need to be sampled?

n = 1,784

If we are performing a two-tailed test of whether μ= 100, the probability of detecting a shift of the mean to 105 will be ________ the probability of detecting a shift of the mean to 110

less than

In hypothesis testing if the null hypothesis is rejected,

the alternative hypothesis is true

In hypothesis testing if the null hypothesis has been rejected when the alternative hypothesis has been true,

the correct decision has been made

In the hypothesis testing procedure, α is

the level of significance

Which of the following does not need to be known in order to compute the p-value?

the level of significance

Which of the following would be an appropriate null hypothesis?

the mean of a population is equal to 55

Referring to table 9-3, the parameter of interest is

the mean power consumption of all such microwave ovens

For a two-tail test, the p-value is the probability of obtaining a value for the test statistic as

unlikely as that provided by the sample

The p-value is a probability that measures the support (or lack of support) for the

null hypothesis

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X = 19.8 and s 2 = 25. Estimate the mean number of admissions per 24-hour period with a 95% confidence interval

19.8 ± 1.249

For a two-tailed test at 98.4% confidence, Z =

2.41

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

2.7970.

The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The value of the test statistic in this problem is approximately equal to

2.80

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

both of the above

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The director randomly selects 64 different 24-hour periods and determines the number of admissions for each. For this sample, X = 19.8 and s 2 = 25. If the director wishes to estimate the mean number of admissions per 24-hour period to within 1 admission with 99% reliability, what size sample should she choose?

n = 166

In hypothesis testing, the tentative assumption about the population parameter is

the null hypothesis

If the p value is less than α in a two-tailed test then:

the null hypothesis should be rejected.

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average 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?

n = 1537

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The rental chain's conclusion from the hypothesis test using a 3% level of significance is:

to open a new store

A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 5,000 of the 20,000 households in the area are equipped with videocassette recorders (VCRs). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCRs. The decision on the hypothesis test using a 3% level of significance is:

to reject H0 in favor of H1 .

For a one-tailed test (lower tail) at 93.7% confidence, Z =

-1.53

The school's newspaper reported that the proportion of students majoring in business is more than 30%. You plan on taking a sample to test the newspaper's claim. The correct set of hypotheses is

H0: P <= 0.30 Ha: P > 0.30

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and = 25 grams. What is the probability that a randomly selected vitamin will contain between 82 and 100 grams of pyridoxine?

0.2132

In a two-tailed hypothesis test the test statistic is determined to be Z = -2.5. The p-value for this test is

0.0124

For a two-tailed test, a sample of 20 at 80% confidence, t =

1.328

You know that the level of significance ( α ) of a test is 5%, you can tell that the probability of committing a Type II error ( β ) is A) 2.5%. B) 95%. C) 97.5%. D) unknown

95%

A sample of 250 people resulted in a confidence interval estimate for the proportion of people who believe that the federal government's proposed tax increase is justified is between 0.14 and 0.20. Based on this information, what was the confidence level used in this estimation?

Approximately 79 percent

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is:

H0: μ = 1200 vs. H1: μ > 1200

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles, which of the following would be the correct formulation of the null and alternative hypotheses?

Ho: µ = 16 Ha: µ ≠ 16

A random sample of 8 observations was drawn from a normal population. The sample mean and sample standard deviation are 40 and 10 respectively. Estimate the population mean with 95% confidence (to 2 decimals).

(31.64, 48.36)

A random sample of 8 observations was drawn from a normal population. The sample mean and population standard deviation are 40 and 10 respectively. Estimate the population mean with 95% confidence (to 2 decimals)

(33.07, 46.93)

A 90% confidence interval is found to be: $6.72 +- 2.38 $4.34 ----- $9.10 Which is the best statement?

Based on the sample data, we are 90% confident the population mean will be between $4.34 and $9.10.

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. What are the appropriate hypotheses to test?

H00 : μ ≤ 30 and H1 : μ > 30

referring to table 9-3, the appropriate hypothesis to determine if the manufacturer's claim appears reasonable are:

H0: 250 versus H1: 250

Your investment executive claims that the average yearly rate of return on the stocks she recommends is more than 10.0%. You plan on taking a sample to test her claim. The correct set of hypotheses is

H0: μ <= 10.0% Ha: μ > 10.0%

Confidence Interval Estimation

It is used to construct confidence intervals for the population mean when the population standard deviation is known.

Which of the following is NOT true about the Student's t distribution?

It is used to construct confidence intervals for the population mean when the population standard deviation is known.

The reason for using the t-distribution in a hypothesis test about the population mean is:

The pop standard deviation is unknown

Which of the following would be an appropriate null hypothesis?

The population proportion is no less than 0.65.

For a lower tail test, the p-value is the probability of obtaining a value for the test statistic

at least as small as that provided by the sample

A house cleaning service claims that it can clean a four bedroom house in less than 2 hours. A sample of n = 16 houses is taken and the sample mean is found to be 1.97 hours and the sample standard deviation is found to be 0.1 hours. Using a 0.05 level of significance the correct conclusion is:

To not reject the null because the test statistic (-1.2) is > the critical value (-1.7531).

True or False: For a given level of significance, if the sample size is increased, the power of the test will increase

True

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

A major department store chain is interested in estimating the average 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 analyzed with the following results: X = $50.50 and s 2 = 400 . Assuming the distribution of the amount spent on their first visit is approximately normal, what is the shape of the sampling distribution of the sample mean that will be used to create the desired confidence interval for

A t distribution with 14 degrees of freedom

When the p-value is used for hypothesis testing, the null hypothesis is rejected if

p-value < = α

The power of a test is measured by its capability of

rejecting a null hypothesis that is false.

Which of the following would be an appropriate null hypothesis?

The mean of the population is equal to 55

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

$15,364

The level of significance

is (1 - confidence level)

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

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 X = 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 ± $119.586

Woof Chow Dog Food Company believes that it has a market share of 25%. They survey n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food, and 23 people say yes. Based upon this information, what is the value of the test statistic?

-0.462

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with μ = 110 grams and σ = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 110 grams of pyridoxine?

0.1554

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and = 25 grams. What is the probability that a randomly selected vitamin will contain between 100 and 120 grams of pyridoxine?

0.3108

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and = 25 grams. What is the probability that a randomly selected vitamin will contain less than 100 grams of pyridoxine?

0.3446

The amount of pyridoxine (in grams) in a multiple vitamin is normally distributed with = 110 grams and = 25 grams. What is the probability that a randomly selected vitamin will contain at least 100 grams of pyridoxine?

0.6554

Referring to Table 9-1, what critical value should the biologist use to determine the rejection region?

1.3006

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.10 level of significance and a random sample of n = 64 bottles which of the following would be the upper tail critical value?

1.645

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 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. Referring to Table 8-3, the confidence interval goes from ________ to ________.

12.09 to 12.19

A confidence interval was use to estimate the proportion of statistics students that are females. A random sample of 72 students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what size sample would be necessary if we wanted to estimate the true proportion within +- 0.08 using 95% confidence?

150

A company that makes shampoo wants to test whether the average amount of shampoo per bottle is 16 ounces. The standard deviation is known to be 0.20 ounces. Assuming that the hypothesis test is to be performed using 0.05 level of significance and a random sample of n = 64 bottles, how large could the sample mean be before they would reject the null hypothesis [i.e. testing H0: (mew) = 16, Ha: (not equal to) 16]

16.049 ounces

What sample size is needed to estimate a population mean within ±50 of the true mean value using a confidence level of 95%, if the true population variance is known to be 122,500?

189

A quality control engineer is interested in the mean length of sheet insulation being cut automatically by machine. The desired length of the insulation is 12 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. Referring to Table 8-3, the critical value to use in obtaining the confidence interval is ________.

2.58

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

2.7970

The Hilbert Drug Store owner plans to survey a random sample of his customers with the objective of estimating the mean dollars spent on pharmaceutical products during the past three months. He has assumed that the population standard deviation is known to be $15.50. Given this information, what would be the required sample size to estimate the population mean with 95 percent confidence and a margin of error of ±$2.00?

231

The file Danish Coffee contains a random sample of 144 Danish coffee drinkers and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase Danish coffee consumption. Based on the sample's results, what is the best point estimate of average annual coffee consumption for Danish coffee drinkers?

6.5368

The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. Table 8-2, they should sample ________ employees if they want to estimate the mean score of the employees within 5 points with 90% confidence

63

The managers of a company are worried about the morale of their employees. In order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points. Referring to Table 8-2, due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88.0 points. A 90% confidence interval would go from ________ to ________.

82.12 to 93.88

In a hypothesis test involving a population mean, which of the following would be an acceptable formulation?

H0 : = $1,700 Ha : > $1,700

Woof Chow Dog Food Company believes that it has a market share of 25 percent. It surveys n = 100 dog owners and ask whether or not Woof Chow is their regular brand of dog food. The appropriate null and alternate hypotheses are:

H0 : p = .25 Ha : p ≠.25

A confidence interval was use to estimate the proportion of statistics students that are females. A random sample of 72 students generated the following 90% confidence interval: (0.438, 0.642). Based on the interval score, is the population proportion of females equal to 0.60?

Maybe. 0.60 is a believable value of the population proportion based on the information above

The R.D. Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by the machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: 14.25 13.7 14.02 14.13 13.99 14.04 Which of the following would be the correct null hypothesis if the company wishes to test the machine?

Mu=14

The R.D. Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by the machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed: Based on these sample data, which of the following is true if the significance level is .05?

The null hypothesis cannot be rejected since the test statistic is approximately t = 0.20, which is not in the rejection region.

If the variance of the contents of cans of orange juice is significantly more than 0.003, the manager has to order to stop the filling machine. A sample of 26 cans of orange juice showed a standard deviation of 0.06 ounces. Based on the sample and at the 0.05 level of significance, the filling machine should be

stopped

Suppose a 95% confidence interval for has been constructed. If it is decided to take a larger sample and to decrease the confidence level of the interval, then the resulting interval width would . (Assume that the sample statistics gathered would not change very much for the new sample.)

be narrower than the current interval width

The cost of a college education has increased at a much faster rate than costs in general over the past twenty years. In order to compensate for this, many students work part- or full-time in addition to attending classes. At one university, it is believed that the average hours students work per week exceeds 20. To test this at a significance level of 0.05, a random sample of n = 20 students was selected and the following values were observed Based on these sample data, the critical value expressed in hours

is approximately equal to 25.26 hours

The chamber of commerce in a beach resort town wants to estimate the proportion of visitors who are repeat visitors. From previous experience they believe the portion is in the vicinity of 0.5 and they want to estimate the proportion to within ± 0.03 percentage points with 95 percent confidence. The sample size they should use is:

n=1068

In the construction of confidence intervals, if all other quantities are unchanged, an increase in the sample size will lead to an interval that's..

narrower

Microsoft Excel was used on a set of data involving the number of parasites found on 46 Monarch butterflies captured in Pismo Beach State Park. A biologist wants to know if the mean number of parasites per butterfly is over 20. She will make her decision using a test with a level of significance of 0.10. The following information was extracted from the Microsoft Excel output for the sample of 46 Monarch butterflies: n = 46; Arithmetic Mean = 28.00; Standard Deviation = 25.92; Standard Error = 3.82; Null Hypothesis: H0 : <=20.000; a = 0.10; df = 45; T Test Statistic = 2.09; One-Tailed Test Upper Critical Value = 1.3006; p-value = 0.021; Decision = Reject Referring to Table 9-1, the parameter the biologist is interested in is:

the mean number of parasites on Monarch butterflies in Pismo Beach State Park

if the p value is less than a in a two-tailed test,

the null hypothesis should be rejected.

When determining the sample size necessary for estimating the true population mean, which factor is NOT considered when sampling with replacement?

the population size

An appliance manufacturer claims to have developed a compact microwave oven that consumes an average of no more than 250 W. From previous studies, it is believed that power consumption for microwave ovens is normally distributed with a standard deviation of 15 W. A consumer group has decided to try to discover if the claim appears true. They take a sample of 20 microwave ovens and find that they consume an average of 257.3 W. Referring to table 9-3, the population of interest is

the power consumption in a such microwave ovens

If a hypothesis is not rejected at the 5% level of significance, it

will also not be rejected at the 1% level

If a hypothesis is rejected at 95% confidence, it

will always be rejected at 90% confidence

An economist is interested in studying the incomes of consumers in a particular region. The population standard deviation is known to be $1,000. A random sample of 50 individuals resulted in an average income of $15,000. What is the width of the 90% confidence interval?

$465.23

A major department store chain is interested in estimating the average 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 analyzed with the following results: $50.50 X = and s 2 = 400 . Construct a 95% confidence interval for the average amount its credit card customers spent on their first visit to the chain's new store in the mall assuming that the amount spent follows a normal distribution

$50.50 +- $11.08

For a one-tailed test (lower tail) with 22 degrees of freedom at 95% confidence, the value of t =

-1.717

The academic planner of a university thinks that at least 35% of the entire student body attends summer school. The correct set of hypotheses to test his belief is

. H0: P >= 0.35 Ha: P < 0.35

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 ± 0.057 or 0.533 ≤ (Pie symbol) ≤ 0.647

The probability of rejecting a false null hypothesis is equal to

1 - β

For a two-tailed test at 86.12% confidence, Z =

1.48

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. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant for a 95% confidence interval, approximately how large a sample did her assistant use to determine the interval estimate?

11

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

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. If the head librarian knows that the population standard deviation is 150 books checked out per day, and she asked her assistant to use 25 days of data to construct the interval estimate, what confidence level can she attach to the interval estimate?

99.7%

If an economist wishes to determine whether there is evidence that the average family income in a community exceeds $25,000, what kind of test should be used?

A one-tailed test should be utilized

If an economist wishes to determine whether there is evidence that the average family income in a community equals $25,000. What kind of test should be used?

A two-tailed test should be utilized

A contract calls for the mean diameter of a cylinder to be 1.50 inches. As a quality check, each day a random sample of n = 36 cylinders is selected and the diameters are measured. Assuming that the population standard deviation is thought to be 0.10 inch and that the test will be conducted using an alpha equal to 0.025, what would the probability of a Type II error be?

Can't be determined without knowing the "true" population mean

In the past, 75% of the tourists who visited Chattanooga went to see Rock City. The management of Rock City recently undertook an extensive promotional campaign. They are interested in determining whether the promotional campaign actually increased the proportion of tourists visiting Rock City. The correct set of hypotheses is

H0: P <= 0.75 Ha: P > 0.75

The average life expectancy of tires produced by the Whitney Tire Company has been 40,000 miles. Management believes that due to a new production process, the life expectancy of their tires has increased. In order to test the validity of their belief, the correct set of hypotheses is

H0: μ <= 40,000 Ha: μ > 40,000

The manager of an automobile dealership is considering a new bonus plan in order to increase sales. Currently, the mean sales rate per salesperson is five automobiles per month. The correct set of hypotheses for testing the effect of the bonus plan is

H0: μ <= 5 Ha: μ > 5

A soft drink filling machine, when in perfect adjustment, fills the bottles with 12 ounces of soft drink. Any over filling or under filling results in the shutdown and readjustment of the machine. To determine whether or not the machine is properly adjusted, the correct set of hypotheses is

H0: μ = 12 Ha: μ ≠ 12

A weatherman stated that the average temperature during July in Chattanooga is less than 80 degrees. A sample of 32 Julys is taken. The correct set of hypotheses is

H0: μ >= 80 Ha: μ < 80

A student believes that the average grade on the final examination in statistics is at least 85. She plans on taking a sample to test her belief. The correct set of hypotheses is

H0: μ >= 85 Ha: μ < 85

Suppose a 95% confidence interval for μ turns out to be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference.

In repeated sampling, 95% of the intervals constructed would contain the population mean.

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 draw?

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

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 s≠16 at α s=0.05?

Reject H0 in favor of H 1

You have created a 95% confidence interval for μ with the result 10≤ μ ≤15. What decision will you make if you test H00: μ =16 versus H11: μ s≠16 at α s=0.10?

Reject H0 in favor of H1

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average 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. Suppose the alternative we wanted to test was H1: < 60. State the correct rejection region for = 0.05

Reject H0: if t<- 1.6604

Which of the following would be an appropriate null hypothesis?

The mean of a population is equal to 55.

Which of the following would be an appropriate alternative hypothesis?

The mean of a population is greater than 55.

Which of the following would be an appropriate alternative hypothesis?

The population proportion is less than 0.65.

A manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you were to conduct a test to determine whether the average balance is different from $75 and decided to reject the null hypothesis, what conclusion could you draw?

There is evidence that the average balance is not $75.

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

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30 and decided not to reject the null hypothesis, what conclusion could you draw?

There is not sufficient evidence that the proportion is not 0.30

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. The 95% confidence interval for (pie symbol) is 0.59 ± 0.07. Interpret this interval

We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.

The marketing manager for an automobile manufacturer is interested in determining the proportion of new compact-car owners who would have purchased a passenger-side inflatable air bag if it had been available for an additional cost of $300. The manager believes from previous information that the proportion is 0.30. Suppose that a survey of 200 new compact-car owners is selected and 79 indicate that they would have purchased the inflatable air bags. If you were to conduct a test to determine whether there is evidence that the proportion is different from 0.30, which test would you use?

Z-test of a population proportion

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average 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. Suppose the test statistic does fall in the rejection region at 0.05. Which of the following decisions is correct?

at 0.05, we reject H0

The power curve provides the probability of

correctly rejecting the null hypothesis

For a given sample size n, if the level of significance is decreased, the power of the test will:

decrease

When determining the sample size for a proportion for a given level of confidence and sampling error, the closer to 0.50 that π is estimated to be, the sample size required ________.

larger

A university system enrolling hundreds of thousands of students is considering a change in the way students pay for their education. Currently, the students pay $55 per credit hour. The university system administrators are contemplating charging each student a set fee of $750 per quarter, regardless of how many credit hours each takes. To see if this proposal would be economically feasible, the administrators would like to know how many credit hours, on the average, each student takes per quarter. A random sample of 250 students yields a mean of 14.1 credit hours per quarter and a standard deviation of 2.3 credit hours per quarter. Suppose the administration wanted to estimate the mean to within 0.1 hours at 95% reliability and assumed that the sample standard deviation provided a good estimate for the population standard deviation. How large a total sample would they need to take?

n = 2033

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

narrower for 90% confidence than for 95% confidence.

The level of significance in hypothesis testing is the probability of

rejecting a true null hypothesis

A two-tailed test is performed at 95% confidence. The p-value is determined to be 0.09. The null hypothesis

should not be rejected

How many Kleenex should the Kimberly Clark Corporation package of tissues contain? Researchers determined that 60 tissues is the average 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 manager of the credit department for an oil company would like to determine whether the average monthly balance of credit card holders is equal to $75. An auditor selects a random sample of 100 accounts and finds that the average owed is $83.40 with a sample standard deviation of $23.65. If you wanted to test whether the auditor should conclude that there is evidence that the average balance is different from $75, which test would you use?

t-test of a population mean