1 A marketing firm is asked to estimate the percentage of existing customers who would purchase a digital upgrade to their basic cable TV service The firm wants 99 percent confidence and an error of 5 percent What is the required sample size (to the next higher integer) a 664 b 625 c 801 d 957 2 Of 200 youthful gamers (under 18) who tried the new Z Box Plus game, 160 rated it excellent, compared with only 144 of 200 adult gamers (18 or over) Calculate the 95 percent confidence interval for the difference of proportions a 013, 263 b 014, 188 c 003, 163 d 057, 261 3 Which is not a likely reason to choose the z distribution for a hypothesis test of a mean a The value of is known b The sample size n is very large c The population is normal d The value of is very large 4 The critical value in a hypothesis test a is calculated from the sample data b usually is 05 or 01 in most statistical tests c separates the acceptance and rejection regions d depends on the value of the test statistic 5 During a test period, an experimental group of 10 vehicles using an 85 percent ethanol gasoline mixture showed mean CO 2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds A control group of 14 vehicles using regular gasoline showed mean CO 2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds Assuming equal variances, the pooled variance is a 296 59 b 225 00 c 400 00 d 522 16 6 A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2 8 minutes with a standard deviation of 1 2 minutes The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is a 0 639 b 0 588 c 0 300 d 2 131 7 Based on a random sample of 13 tire changes, the mean time to change a tire on a Boeing 777 has a mean of 59 5 minutes with a standard deviation of 8 4 minutes For 10 tire changes on a Boeing 787, the mean time was 64 3 minutes with a standard deviation of 12 4 minutes To test for equal variances in a two tailed test at 10, the critical values are a 3 73 and 0 228 b 2 51 and 3 67 c 3 07 and 0 398 d 3 07 and 0 357 8 Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours Aha she cried, the average stay exceeds the guideline The value of the test statistic for her hypothesis is a 2 080 b 0 481 c 1 866 d 2 000 9 Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the variance in the time it takes to perform an appendectomy A sample of 8 appendectomies using the old method had a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a variance of 16 minutes At 10 in a two tailed test for equal variances, the critical values are a 0 272 and 3 29 b 0 299 and 3 07 c 0 368 and 2 51 d 1 645 and 1 645 10 Hypothesis tests for a mean using the critical value method require a using a two tailed test b sampling a normal population c knowing the true population mean d specifying in advance 11 Assuming that 50 is a quick and conservative approach to use in a sample size calculation for a proportion Select one True False 12 In a large lecture class, the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87 Using the Empirical Rule 3 to estimate , how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of 2 a about 17 students b about 35 students c about 188 students d about 25 students 13 The conservative sample size required for a 95 percent confidence interval for with an error of 0 04 is a 271 b 423 c 385 d 601 14 If 12, find the sample size to estimate the mean with an error of 4 and 95 percent confidence (rounded to the next higher integer) a 75 b 35 c 58 d 113 15 At Huge University, a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree, compared with 120 of 800 arts and sciences seniors We want to know if the proportion is higher in the arts and sciences group What is the z test statistic a 1 322 b 1 122 c 0 716 d We must first know 16 The Central Limit Theorem guarantees an approximately normal sampling distribution for the mean when n is sufficiently large Select one True False 17 A university wants to estimate the average distance that commuter students travel to get to class with an error of 3 miles and 90 percent confidence What sample size would be needed, assuming that travel distances are normally distributed with a range of X 0 to X 50 miles, using the Empirical Rule 3 to estimate a about 28 students b about 47 students c about 30 students d about 21 students 18 A high confidence level ensures that the confidence interval will enclose the true parameter of interest Select one True False 19 In a two tailed test, a statistician got a z test statistic of 1 47 What is the p value a 0708 b 1416 c 0874 d 0301 20 The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gram The process standard deviation is known to be 0 77 gram A random sample of 49 candy bars yields a mean weight of 55 82 gram Find the p value for a test to see whether the candy bars are smaller than they are supposed to be a Between 05 and 10 b Between 025 and 05 c Between 01 and 025 d Less than 01 21 Which is not a type of comparison for which you would anticipate a two sample test a Before Treatment versus After Treatment b Old Method versus New Method c Sample Mean versus Desired Mean d Experimental Group versus Control Group 22 Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes For a right tailed test of means (assume equal variances), the test statistic is a 3 814 b 2 365 c 3 000 d 1 895 23 The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gram The process standard deviation is known to be 0 77 gram A random sample of 49 candy bars yields a mean weight of 55 82 gram Find the test statistic to see whether the candy bars are smaller than they are supposed to be a 1 636 b 1 645 c 1 677 d 1 636 24 A new policy of flex hours is proposed Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change Management wonders if there is a difference between the two groups What is the p value for a two tailed test a 3849 b 1151 c 2301 d 3453 25 I believe your airplane's engine is sound, states the mechanic I've been over it carefully, and can't see anything wrong I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500 But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone If the pilot decides to have the mechanic perform the internal inspection, the cost of Type I error is a the pilot will experience the thrill of no engine flight b the pilot will be out $1,500 unnecessarily c the mechanic will lose a good customer d impossible to determine without knowing 26 Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy JBGHI demands a sample large enough to ensure an error of 2 percent with 90 percent confidence What is the necessary sample size a 4,148 b 2,401 c 1,692 d 1,604 27 The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it A trial sample of 25 employees shows that 16 are dissatisfied The p value for a right tailed test is a 0 1337 b 0 4192 c 0 0901 d 0 0808 28 In a test for equality of two proportions, the sample proportions were p 1 12 50 and p 2 18 50 The test statistic is a 1 44 b 1 31 c 1 67 d Impossible to determine without knowing 29 During a test period, an experimental group of 10 vehicles using an 85 percent ethanol gasoline mixture showed mean CO 2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds A control group of 14 vehicles using regular gasoline showed mean CO 2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds At 05, in a left tailed test (assuming equal variances) the test statistic is a 1 310 b 2 042 c 1 645 d 1 683 30 My careful physical examination shows no evidence of any serious problem, said Doctor Morpheus However, a very costly lab test can be performed to check for the rare condition known as estomalgia fatalis The test is almost invariably negative for persons with your age and symptoms My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce But you must decide for yourself Agreeing that the doctor's hypothesis is true, you decide to forgo the expensive lab test What would be the consequence of Type II error on your part a It cannot be determined without knowing the type of test b Your estomalgia fatalis will go undetected c You will pay for a lab test that agrees with the doctor d Your survivors will enjoy a sizeable malpractice award

The Answer is in the image, click to view ...

Answered step by step

Verified Expert Solution

Link Copied!

Question

1 Approved Answer

Posted on Jun 26, 2024

1. A marketing firm is asked to estimate the percentage of existing customers who would purchase a digital upgrade to their basic cable TV service.

A marketing firm is asked to estimate the percentage of existing customers who would purchase a "digital upgrade" to their basic cable TV service. The firm wants 99 percent confidence and an error of 5 percent. What is the required sample size (to the next higher integer)?

664

625

801

957

Of 200 youthful gamers (under 18) who tried the new Z-Box-Plus game, 160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over). Calculate the 95 percent confidence interval for the difference of proportions.

[+.013, +.263]

[.014, +.188]

[.003, +.163]

[+.057, +.261]

Which isnota likely reason to choose thezdistribution for a hypothesis test of a mean?

The value ofis known.

The sample sizenis very large.

The population is normal.

The value ofis very large.

The critical value in a hypothesis test

is calculated from the sample data.

usually is .05 or .01 in most statistical tests.

separates the acceptance and rejection regions.

depends on the value of the test statistic.

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO₂emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO₂emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. Assuming equal variances, the pooled variance is

296.59.

225.00.

400.00.

522.16.

A random sample of 16 ATM transactions at the Last National Bank of Flat Rock revealed a mean transaction time of 2.8 minutes with a standard deviation of 1.2 minutes. The width (in minutes) of the 95 percent confidence interval for the true mean transaction time is

0.639.

0.588.

0.300.

2.131.

Based on a random sample of 13 tire changes, the mean time to change a tire on a Boeing 777 has a mean of 59.5 minutes with a standard deviation of 8.4 minutes. For 10 tire changes on a Boeing 787, the mean time was 64.3 minutes with a standard deviation of 12.4 minutes. To test for equal variances in a two-tailed test at= .10, the critical values are

3.73 and 0.228.

2.51 and 3.67.

3.07 and 0.398.

3.07 and 0.357.

Guidelines for the Jolly Blue Giant Health Insurance Company say that the average hospitalization for a triple hernia operation should not exceed 30 hours. A diligent auditor studied records of 16 randomly chosen triple hernia operations at Hackmore Hospital and found a mean hospital stay of 40 hours with a standard deviation of 20 hours. "Aha!" she cried, "the average stay exceeds the guideline." The value of thetest statisticfor her hypothesis is

2.080.

0.481.

1.866.

2.000.

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the variance in the time it takes to perform an appendectomy. A sample of 8 appendectomies using the old method had a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a variance of 16 minutes. At= .10 in a two-tailed test for equal variances, the critical values are

0.272 and 3.29.

0.299 and 3.07.

0.368 and 2.51.

1.645 and +1.645.

10.

Hypothesis tests for a mean using the critical value method require

using a two-tailed test.

sampling a normal population.

knowing the true population mean.

specifyingin advance.

11.

Assuming that= .50 is a quick and conservative approach to use in a sample size calculation for a proportion.

Select one:

True

False

12.

In a large lecture class, the professor announced that the scores on a recent exam were normally distributed with a range from 51 to 87. Using the Empirical Rule 3to estimate, how many students would you need to sample to estimate the true mean score for the class with 90 percent confidence and an error of 2?

about 17 students

about 35 students

about 188 students

about 25 students

13.

The conservative sample size required for a 95 percent confidence interval forwith an error of 0.04 is

271.

423.

385.

601.

14.

If= 12, find the sample size to estimate the mean with an error of 4 and 95 percent confidence (rounded to the next higher integer).

113

15.

At Huge University, a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree, compared with 120 of 800 arts and sciences seniors. We want to know if the proportion is higher in the arts and sciences group. What is theztest statistic?

1.322.

1.122.

0.716.

We must first know.

16.

The Central Limit Theorem guarantees an approximately normal sampling distribution for the mean whennis sufficiently large.

Select one:

True

False

17.

A university wants to estimate the average distance that commuter students travel to get to class with an error of 3 miles and 90 percent confidence. What sample size would be needed, assuming that travel distances are normally distributed with a range ofX= 0 toX= 50 miles, using the Empirical Rule 3to estimate.

about 28 students

about 47 students

about 30 students

about 21 students

18.

A high confidence level ensures that the confidence interval will enclose the true parameter of interest.

Select one:

True

False

19.

In a two-tailed test, a statistician got aztest statistic of 1.47. What is thep-value?

.0708

.1416

.0874

.0301

20.

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gram. The process standard deviation is known to be 0.77 gram. A random sample of 49 candy bars yields a mean weight of 55.82 gram. Find thep-value for a test to see whether the candy bars are smaller than they are supposed to be.

Between .05 and .10.

Between .025 and .05.

Between .01 and .025.

Less than .01.

21.

Which isnota type of comparison for which you would anticipate a two-sample test?

Before TreatmentversusAfter Treatment.

Old MethodversusNew Method.

Sample MeanversusDesired Mean.

Experimental GroupversusControl Group.

22.

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test of means (assume equal variances), the test statistic is

3.814.

2.365.

3.000.

1.895.

23.

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gram. The process standard deviation is known to be 0.77 gram. A random sample of 49 candy bars yields a mean weight of 55.82 gram. Find thetest statisticto see whether the candy bars are smaller than they are supposed to be.

1.636

1.645

1.677

+1.636

24.

A new policy of "flex hours" is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. What is thep-value for a two-tailed test?

.3849

.1151

.2301

.3453

25.

"I believe your airplane's engine is sound," states the mechanic. "I've been over it carefully, and can't see anything wrong. I'd be happy to tear the engine down completely for an internal inspection at a cost of $1,500. But I believe that roughness you heard in the engine on your last flight was probably just a bit of water in the fuel, which passed harmlessly through the engine and is now gone." If the pilot decides to have the mechanic perform the internal inspection, the cost of Type I error is

the pilot will experience the thrill of no-engine flight.

the pilot will be out $1,500 unnecessarily.

the mechanic will lose a good customer.

impossible to determine without knowing.

26.

Jolly Blue Giant Health Insurance (JBGHI) is concerned about rising lab test costs and would like to know what proportion of the positive lab tests for prostate cancer are actually proven correct through subsequent biopsy. JBGHI demands a sample large enough to ensure an error of 2 percent with 90 percent confidence. What is the necessary sample size?

4,148

2,401

1,692

1,604

27.

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. Thep-value for a right-tailed test is

0.1337.

0.4192.

0.0901.

0.0808.

28.

In a test for equality of two proportions, the sample proportions werep₁= 12/50 andp₂= 18/50. The test statistic is

1.44.

1.31.

1.67.

Impossible to determine without knowing.

29.

1.310.

2.042.

1.645.

1.683.

30.

"My careful physical examination shows no evidence of any serious problem," said Doctor Morpheus. "However, a very costly lab test can be performed to check for the rare condition known asestomalgia fatalis. The test is almost invariably negative for persons with your age and symptoms. My personal hypothesis is that the occasional stomach pain you reported is due to indigestion caused by eating tacos with too much hot sauce. But you must decide for yourself." Agreeing that the doctor's hypothesis is true, you decide to forgo the expensive lab test. What would be the consequence of Type II error on your part?

It cannot be determined without knowing the type of test.

Yourestomalgia fataliswill go undetected.

You will pay for a lab test that agrees with the doctor.

Your survivors will enjoy a sizeable malpractice award.