A+ Answers



A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the null and alternative hypotheses for the test described.

 

A. H0: µ = 16 ounces     Ha: µ < 16 ounces   

B. H0: µ ¹ 16 ounces     Ha: µ = 16 ounces    

C. H0: µ = 16 ounces     Ha: µ > 16 ounces   

D. H0: µ = 16 ounces      Ha: µ ¹ 16 ounces   

In 1990, the average duration of long-distance telephone calls originating in one town was 9.3 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 9.3 minutes. Formulate the null and alternative hypotheses for the study described.

 

A. Ho: µ = 9.3 minutes     H a : µ < 9.3 minutes       

B. Ho: µ = 9.3 minutes     H a : µ > 9.3 minutes       

C. Ho: µ = 9.3 minutes      H a : µ ¹ 9.3 minutes       

D. Ho: µ ¹ 9.3 minutes     H a : µ = 9.3 minutes        

A right-tailed test is conducted at the 5% significance level. Which of the following z-scores is the smallest one in absolute value that leads to rejection of the null hypothesis?  

A. 1.61            

B. 1.85 

C. -1.98           

D. -2.06           

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.       

A researcher claims that the amounts of acetaminophen in a certain brand of cold tablets have a mean different from the 600 mg claimed by the manufacturer. Test this claim at the 0.02 level of significance. The mean acetaminophen content for a random sample of n = 41 tablets is 603.3 mg. Assume that the population standard deviation is 4.9 mg.

A. Since the test statistic is greater than the critical z, there is sufficient evidence to accept the null hypothesis and to support the claim that the mean content of acetaminophen is 600 mg.      

B. Since the test statistic is greater than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.           

C. Since the test statistic is less than the critical z, there is sufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.      

D. Since the test statistic is greater than the critical z, there is insufficient evidence to reject the null hypothesis and to support the claim that the mean content of acetaminophen is not 600 mg.           

 

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.           

A study of a brand of “in the shell peanuts” gives the following results:

 

A significant event at the 0.01 level is a fan getting a bag with how many peanuts?

A. 30 peanuts  

B. 25 or 30 peanuts     

C. 25 or 55 peanuts     

D. 25 peanuts  

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

            

The owner of a football team claims that the average attendance at home games is over 3000, and he is therefore justified in moving the team to a city with a larger stadium. 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 mean attendance is greater than 3000.   

B. There is sufficient evidence to support the claim that the mean attendance is equal to 3000.   

C. There is not sufficient evidence to support the claim that the mean attendance is greater than 3000.       

D. There is not sufficient evidence to support the claim that the mean attendance is less than 3000.       

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        

 

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          

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      

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 15 of 40       2.5 Points

 

without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.

 A. is less than 1 standard deviation above the claimed mean.         

 

B.  is more than 4 standard deviations above the claimed mean.     

 

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

 

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

            

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     

 

A consumer advocacy group claims that the mean amount of juice in a 16 ounce bottled drink is not 16 ounces, as stated by the bottler. Determine the conclusion of the hypothesis test assuming that the results of the sampling lead to rejection of the null hypothesis.

A. Conclusion: Support the claim that the mean is equal to 16 ounces.       

B. Conclusion: Support the claim that the mean is greater than 16 ounces. 

C. Conclusion: Support the claim that the mean is not equal to 16 ounces. 

D. Conclusion: Support the claim that the mean is less than 16 ounces.     

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO is less than 1 in every one thousand. State the null hypothesis and the alternative hypothesis for a test of significance.

A. H0: p = 0.001     Ha: p > 0.001      

B. H0: p = 0.001      Ha: p < 0.001     

C. H0: p > 0.001     Ha: p = 0.001      

D. H0: p < 0.001     Ha: p = 0.001      

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..    

 

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.      

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.

A. Colorblind Male 4.8; Not Colorblind Male 55.2  

B. Colorblind Male 6.8; Not Colorblind Male 53.2  

C. Colorblind Male 4.8; Not Colorblind Male 55.4  

D. Colorblind Male 4.8; Not Colorblind Male 56.2  

 

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 female combinations of gender and colorblindness.

A. Colorblind Female 4.8; Not Colorblind Female 55.2       

B. Colorblind Female 3.2; Not Colorblind Female 36.8       

C. Colorblind Female 4.8; Not Colorblind Female 35.2       

D. Colorblind Female 3.8; Not Colorblind Female 36.2       

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.           

 

A golfer wished to find a ball that would travel more than 170 yards when hit with his 6-iron with a club head speed of 90 miles per hour. He had a golf equipment lab test a low compression ball by having a robot swing his club 12 times at the required speed.

Data from this test had a sample mean of 171.6 yards with a sample standard deviation of 2.4 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

Area in one tail

0.025   0.05

Area in two tails

Degrees of

Freedom

n – 1     0.05     0.10

6          2.447   1.943

7          2.365   1.895

8          2.306   1.860

9          2.262   1.833

 

A. Accept the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.     

B. Accept the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.     

C. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 170 yards.     

D. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 170 yards.     

 

Which of the following statements is true?

A. The t distribution cannot be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.     

B. The t distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.     

C. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.     

D. The p distribution can be used when finding a confidence interval for the population mean with a small sample whenever the sample comes from a symmetric population.

            

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-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 8 times at the required speed. State the null and alternative hypotheses for this test.

A. H0: µ = 160; Ha: µ > 150  

B. H0: µ = 150; Ha: µ > 150  

C. H0: µ = 160; Ha: µ > 160  

D. H0: µ = 140; Ha: µ > 160  

 

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

Find the value of the X2 statistic for the data above.

A. 1.325          

B. 1.318          

C. 1.286          

D. 1.264          

            None of the above answer choices is correct.

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     

 

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       

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 24.8. What is the margin of error?

A. 4.4  

B. 4.6  

C. 4.8  

D. 5.0  

 

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 population variances of the three groups are equal.           

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

 

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

State the null and alternative hypothesis for the information above.

 

A.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are related in some way.     

 

B.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are not related in any way.  

 

C.

H0: Colorblindness and gender are dependent characteristics.

Ha: Colorblindness and gender are not related in any way.  

 

D.

H0: Colorblindness and gender are independent characteristics.

Ha: Colorblindness and gender are related in some way.     

 

A golfer wished to find a ball that would travel more than 160 yards when hit with his 7-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 8 times at the required speed.

Data from this test resulted in a sample mean of 163.2 yards with a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below to solve this problem.

Area in one tail

0.025   0.05

Area in two tails

Degrees of

Freedom

n – 1     0.05     0.10

6          2.447   1.943

7          2.365   1.895

8          2.306   1.860

9          2.262   1.833

 

A.

Do not reject the null hypothesis. The data do not provide sufficient

evidence that the average distance is greater than 160 yards.          

 

B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards.     

 

C. t= 1.2334; Critical value = 1.992  

 

 

D. Insufficient information to answer this question.

            

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

A         B         C

34        27        19

26        23        31

31        29        22

28        21        22

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 population variances of the three groups are equal.           

 

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

 

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 X2 statistic for the data above.

A. 1.463          

B. 1.852          

C. 1.947          

D. 1.949          

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. 

The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2 statistic is 3.427, state your conclusion about the relationship between gender and colorblindness.

A. Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.     

B. Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.     

C. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.     

D. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.     

 

A 95% confidence interval for the mean of a normal population is found to be 15.6 < µ < 25.2. What is the margin of error?

A. 3.9  

B. 4.8  

C. 4.9  

D. 3.7  

One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent.

The critical value of X2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X2  statistic is 3.179, state your conclusion about the relationship between gender and colorblindness.

A. Do not reject H0.   

B. Reject H0.  

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

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

 

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.

Data from this test resulted in a sample mean of 184.2 yards and a sample standard deviation of 5.8 yards. Assuming normality, carry out a hypothesis test at the 0.05 significance level to determine whether the ball meets the golfer’s requirements. Use the partial t-table below.

Area in one tail

0.025   0.05

Area in two tails

Degrees of

Freedom

n – 1     0.05     0.10

6          2.447   1.943

7          2.365   1.895

8          2.306   1.860

9          2.262   1.833

A. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.     

B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.     

C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards.   

D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.   

 

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

If gender and colorblindness are independent, find the expected values corresponding to the four combinations of gender and colorblindness, and enter them in the following table along with row and column totals.

Colorblind      Not Colorblind           Total

Male    65460 

Female            43640 

Total   1090100 

 

A. Male Colorblind 6.0; Male Not Colorblind 54.0  

B. Male Colorblind 7.0; Male Not Colorblind 53.0  

C. Male Colorblind 8.0; Male Not Colorblind 52.0  

D. Male Colorblind 6.0; Male Not Colorblind 53.0