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Statistics

Statistics

Question 1 of 40

2.5 Points

 

The owner of a football team claims that the average attendance at home games is over 4000, and he is therefore justified in moving the team to a city with a larger stadium. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

  A. All games played by the team in question in which the attendance is over 4000          

  B. All future home games to be played by the team in question     

  C. All home games played by the team in question

  D. None of the populations given are appropriate

 

Question 2 of 40

 

2.5 Points

 

Number of Peanuts per bag

Probability

25

0.006

30

0.020

35

0.093

40

0.150

45

0.350

50

0.217

55

0.170

         

If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?

 

 

 

[removed] A. 0.05

 

[removed] B. 0.025

 

 

 

[removed] C. 0.01

 

 

[removed] D. It is not significant at any of the levels given

 

 

 

Question 3 of 40

2.5 Points

 

In the past, the mean running time for a certain type of flashlight battery has been 9.8 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:

 

H0 : µ  = 9.8 hours

Ha : µ  > 9.8 hours

 

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify that conclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean running time has not increased.

 

  A. Type I error         

  B. Type II error        

  C. Correct decision  

  D. Can not be determined from this information

 

Question 4 of 40

2.5 Points

 

A psychologist claims that more than 19 percent of the population suffers from professional problems due to extreme shyness. Assume that a hypothesis test of the claim has been conducted and that the conclusion of the test was to reject the null hypothesis. Identify the population to which the results of the test apply.

  A. The population is all shy workers.           

  B. The population cannot be identified from the description of the study.            

  C. The population is all American workers.

  D. The population is all American professional workers (doctors, lawyers, CPA’s, and the like.. 

 

 Question 5 of 40

2.5 Points

 

A poll of 1,068 adult Americans reveals that 52% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 significance level, test the claim that more than half of all voters prefer the Democrat.

  A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.     

  B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.      

  C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats.     

  D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats.      

 

Question 6 of 40

2.5 Points

 

A nationwide study of American homeowners revealed that 65% have one or more lawn mowers. A lawn equipment manufacturer, located in Omaha, feels the estimate is too low for households in Omaha. Find the P-value for a test of the claim that the proportion with lawn mowers in Omaha is higher than 65%. Among 497 randomly selected homes in Omaha, 340 had one or more lawn mowers. Use Table 5.1 to find the best answer.

  A. 0.0559       B. 0.1118        C. 0.0252        D. 0.0505

 

 

Question 7 of 40

2.5 Points

 

A psychologist claims that more than 29 percent of the professional population suffers from problems due to extreme shyness. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in non-technical terms.

  A. There is sufficient evidence to support the claim that the true proportion is less than 29 percent.        

  B. There is not sufficient evidence to support the claim that the true proportion is greater than 29 percent.         

  C. There is sufficient evidence to support the claim that the true proportion is equal to 29 percent.         

  D. There is sufficient evidence to support the claim that the true proportion is greater than 29 percent.   

 

Question 8 of 40

2.5 Points

 

A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?

  A. Greater than or equal to 0.10      

  B. Less than or equal to 0.05           

  C. Less than or equal to 0.10           

  D. Greater than or equal to 0.05

 

Question 9 of 40

2.5 Points

 

In 1990, the average duration of long-distance telephone calls originating in one town was 9.4 minutes. A long-distance telephone company wants to perform a hypothesis test to determine whether the average duration of long-distance phone calls has changed from the 1990 mean of 9.4 minutes. The mean duration for a random sample of 50 calls originating in the town was 8.6 minutes. Does the data provide sufficient evidence to conclude that the mean call duration, µ, is different from the 1990 mean of 9.4 minutes? Perform the appropriate hypothesis test using a significance level of 0.01. Assume that  = 4.8 minutes.

  A. With a z of  -1.2 there is sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.           

  B. With a P-value of 0.2302 there is not sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.  

  C. With a P-value of 0.2302 there is sufficient evidence to conclude that the mean value is less than the 1990 mean of 9.4 minutes.           

  D. With a z of –1.2 there is not sufficient evidence to conclude that the mean value has changed from the 1990 mean of 9.4 minutes.

 

Question 10 of 40

2.5 Points

 

A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A consumer advocacy group wants to perform a hypothesis test to determine whether the mean amount is actually less than this. The mean volume of juice for a random sample of 70 bottles was 15.94 ounces. Do the data provide sufficient evidence to conclude that the mean amount of juice for all 16-ounce bottles, µ, is less than 16.1 ounces? Perform the appropriate hypothesis test using a significance level of 0.10. Assume that s = 0.9 ounces.  

 

  A. The z of – 1.49 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

  B. The z of – 1.49 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

 C. The z of – 0.1778 does not provide sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

 D. The z of – 0.1778 provides sufficient evidence to conclude that the mean amount of juice is less than 16.1 oz.

 

Question 11 of 40

2.5 Points

 

A two-tailed test is conducted at the 5% significance level. What is the left tail percentile required to reject the null hypothesis?

  A. 97.5%        B. 5%               C. 2.5%           D. 95%

 

Question 12 of 40

2.5 Points

 

In the past, the mean running time for a certain type of flashlight battery has been 8.0 hours. The manufacturer has introduced a change in the production method and wants to perform a hypothesis test to determine whether the mean running time has increased as a result. The hypotheses are:

H0 : µ  = 8.0 hours

Ha : µ  > 8.0 hours

Explain the meaning of a Type II error.

  A. Concluding that µ > 8.0 hours when in fact µ > 8.0 hours         

  B. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ >8.0 hours    

  C. Concluding that µ > 8.0 hours    

  D. Failing to reject the hypothesis that µ = 8.0 hours when in fact µ = 8.0 hours

 

Question 13 of 40

2.5 Points

 

A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?

  A. Greater than or equal to .010      

  B. Greater than or equal to 0.05      

  C. Less than or equal to 0.10           

  D. Less than or equal to 0.05

 

Question 14 of 40

2.5 Points

 

A supplier of DVDs claims that no more than 1% of the DVDs are defective. In a random sample of 600 DVDs, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the 0.01 level of significance, test the supplier’s claim that no more than 1% are defective.

  A. Do not reject the null hypothesis and conclude that there is evidence to support the claim that more than 1% of the DVDs are defective.        

  B. Reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.         

  C. Do not reject the null hypothesis and conclude that there is insufficient evidence to support the claim that more than 1% of the DVDs are defective.

  D. Reject the null hypothesis and conclude that there is sufficient evidence to support the claim that more than 1% of the DVDs are defective

 

Question 15 of 40

2.5 Points

 

A two-tailed test is conducted at the 5% significance level. Which of the z-scores below is the smallest one that leads to rejection of the null hypothesis?

  A. 1.12            B. 1.48           C. 1.84            D. 2.15

 

Question 16 of 40

2.5 Points

 

A consumer group claims that the mean running time for a certain type of flashlight battery is not the same as the manufacturer’s claims. Determine the null and alternative hypotheses for the test described.

  A.

H0: µ = Manufacturer’s claims     Ha: µ < Manufacturer’s claims

B.

H0: µ = Manufacturer’s claims    Ha: µ ¹ Manufacturer’s claims

 C.

H0: µ = Manufacturer’s claims     Ha: µ > Manufacturer’s claims

  D.

H0: µ ¹ Manufacturer’s claims     Ha: µ = Manufacturer’s claims

 

Question 17 of 40

2.5 Points

 

z = 1.8 for Ha:  µ > claimed value. What is the P-value for the test?  

 

  A. 0.9641      B. 3.59             C. 96.41         D. 0.0359

 

Question 18 of 40

2.5 Points

 

Ha: m > 19,  = 23.8, s = 8, n = 100; without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

  A. Ha is not supported,  is less than 1 standard deviation above the claimed mean.

 

  B. Ha is not supported,   is more than 4 standard deviations above the claimed mean.

 

  C. Ha is supported,   is less than 1 standard deviation above the claimed mean.

 

  D. Ha is supported,   is more than 4 standard deviations above the claimed mean.

 

 

Question 19 of 40

2.5 Points

 

At one school, the mean amount of time that tenth-graders spend watching television each week is 18.4 hours. The principal introduces a campaign to encourage the students to watch less television. One year later, the principal wants to perform a hypothesis test to determine whether the average amount of time spent watching television per week has decreased.

Formulate the null and alternative hypotheses for the study described.

 

  A. Ho: µ = 18.4 hours     H a : µ ¹ 18.4 hours

 

  B. Ho: µ = 18.4 hours     H a : µ < 18.4 hours

 

  C. Ho: µ ³ 18.4 hours     H a : µ < 18.4 hours

 

  D. Ho: µ = 18.4 hours     H a : µ > 18.4 hours

 

Question 20 of 40

2.5 Points

 

A long-distance telephone company claims that the mean duration of long-distance telephone calls originating in one town was greater than 9.4 minutes, which is the average for the state. Determine the conclusion of the hypothesis test assuming that the results of the sampling do not lead to rejection of the null hypothesis.

  A. Conclusion: Support the claim that the mean is less than 9.4 minutes.  

  B. Conclusion: Support the claim that the mean is greater than 9.4 minutes.         

  C. Conclusion: Support the claim that the mean is equal to 9.4 minutes.    

  D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes.

 

         

Question 21 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

 

Colorblind

Not Colorblind

Total

Male

8

52

60

Female

2

38

40

Total

10

90

100

Find the value of the χ2 statistic for the data above.

 

 

[removed] 

A. 1.463

 

[removed] 

B. 1.852

 

[removed] 

C. 1.947

 

[removed] 

D. 1.949

 

 

 

Question 22 of 40

2.5 Points

 

Which of the following statements is true?

  A. The p distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.       

  B. The t distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.       

  C. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.       

  D. The p distribution can be used when finding a confidence interval for the population mean with a small sample anytime the population standard deviation is unknown.

 

 

Question 23 of 40

2.5 Points

 

Which of the following statements is true?

  A. The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.

  B. The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small.   

  C. The t distribution cannot be used when finding a confidence interval for the population mean whenever the sample size is small.   

  D. The p distribution cannot be used when finding a confidence interval for the sample mean whenever the sample size is small.

 

 

Question 24 of 40

2.5 Points

A golfer wished to find a ball that would travel more than 180 yards when hit with his 5-iron with a club speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 7 times at the required speed. State the null and alternative hypotheses for this test.

 

 

[removed] A. H0:  µ = 180; Ha:  µ > 180

 

[removed] B. H0: µ > 180; Ha: µ > 180

 

[removed] C. H0: µ < 180; Ha: µ > 180

 

[removed] D. H0: µ = 180; Ha: µ < 180

 

 

 

 

Question 25 of 40

2.5 Points

 

The margin of error in estimating the population mean of a normal population is E = 9.3 when the sample size is 15. If the sample size had been 18 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3? Explain your answer.

 

  A. Smaller. E decreases as the square root of the sample size gets larger.  

  B. Smaller. E increases as the square root of the sample size gets larger.    

  C. Larger. E decreases as the square root of the sample size gets larger.    

  D. Larger. E increases as the square root of the sample size gets larger.

 

 

Question 26 of 40

2.5 Points

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.

 

Colorblind

Not Colorblind

Total

Male

7

53

60

Female

1

39

40

Total

8

92

100

If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.

 

 

[removed] 

A. Colorblind Male 4.8; Not Colorblind Male 55.2

 

[removed] 

B. Colorblind Male 6.8; Not Colorblind Male 53.2

 

[removed] 

C. Colorblind Male 4.8; Not Colorblind Male 55.4

 

[removed] 

D. Colorblind Male 4.8; Not Colorblind Male 56.2

 

 

 

Question 27 of 40

2.5 Points

 

A simple random sample from a normal distribution is taken in order to obtain a 95% confidence interval for the population mean. If the sample size is 8, the sample mean x̄ is 22, and the sample standard deviation s is 6.3, what is the margin of error? Show your answer to 2 decimal places.

 

  A. df = 7; E = 3.3445.38 = 5.6566  

  B. df = 8; E = 3.3445.38 = 5.6566  

  C. df = 6; E = 2.3656.38 = 5.769    

  D. df = 7; E = 2.3656.38 = 5.869

 

 

Question 28 of 40

2.5 Points

The critical value of χ 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ 2 statistic in Problem 8 had been 3.179, state your conclusion about the relationship between gender and colorblindness.

 

 

[removed] A. Do not reject H0.

 

[removed] B. Reject H0.

 

[removed] C. There is sufficient evidence to support the claim that gender and colorblindness are not related.

 

[removed] D. There is not sufficient evidence to accept or reject H0.

 

 

Question 29 of 40

2.5 Points  

 

A large test statistic F tells us that the sample means __________ the data within the individual samples, which would be unlikely if the populations means really were equal (as the null hypothesis claims).

  A. differ more than   B. differ less than       C. are equal to              D. do not vary with

 

 

Question 30 of 40

2.5 Points

 

The following data were analyzed using one-way analysis of variance.

 

A         B         C

34        27        19

26        23        21

31        29        22

28        21        12

Which one of the following statements is correct?

 

  A. The purpose of the analysis is to determine whether the groups A, B, and C are independent.            

  B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal.

  C. The purpose of the analysis is to test the hypothesis that the populati


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