Statistics
justiceps
dec.docx|
Question 1 of 40 |
2.5 Points |
If a fan purchased a bag with 30 peanuts, what is the lowest level at which this would be a significant event?
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A. 0.05 |
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B. 0.025 |
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C. 0.01 |
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D. It is not significant at any of the levels given |
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Question 2 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.
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A. All games played by the team in question in which the attendance is over 4000 |
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B. All future home games to be played by the team in question |
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C. All home games played by the team in question |
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D. None of the populations given are appropriate |
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Question 3 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%
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.
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A. H0: µ = 16 ounces Ha: µ < 16 ounces |
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B. H0: µ 16 ounces Ha: µ = 16 ounces |
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C. H0: µ = 16 ounces Ha: µ > 16 ounces |
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D. H0: µ = 16 ounces Ha: µ 16 ounces Question 5 of 40 2.5 Points 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.
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Question 6 of 40
2.5 Points
A researcher wants to check the claim that convicted burglars spend an average of 18.7 months in jail. She takes a random sample of 35 such cases from court files and finds that months. Assume that the population standard deviation is 7 months. Test the null hypothesis that µ = 18.7 at the 0.05 significance level.
A.
Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported.
B.
Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
C.Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported
D.Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported.
Question 7 of 40
2.5 Points
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 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 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 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 11 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 12 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..
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?
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A. 30 peanuts |
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B. 25 or 30 peanuts |
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C. 25 or 55 peanuts |
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D. 25 peanuts |
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n 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 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
Question 16 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 18 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 19 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.
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 21 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
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Question 22 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.
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Colorblind |
Not Colorblind |
Total |
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Male |
7 |
53 |
60 |
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Female |
1 |
39 |
40 |
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Total |
8 |
92 |
100 |
If gender and colorblindness are independent, find the expected values corresponding to the female combinations of gender and colorblindness.
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A. Colorblind Female 4.8; Not Colorblind Female 55.2 |
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B. Colorblind Female 3.2; Not Colorblind Female 36.8 |
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C. Colorblind Female 4.8; Not Colorblind Female 35.2 |
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D. Colorblind Female 3.8; Not Colorblind Female 36.2 |
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Question 23 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 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.
Question 24 of 40
2.5 Points
The __________ test statistic is for the one-way analysis of variance.
A. P-Value
B. t
C. F
D. p
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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.
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Colorblind |
Not Colorblind |
Total |
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Male |
8 |
52 |
60 |
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Female |
2 |
38 |
40 |
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Total |
10 |
90 |
100 |
Find the value of the χ2 statistic for the data above.
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A. 1.463 |
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B. 1.852 |
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C. 1.947 |
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D. 1.949 |
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Question 26 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.
One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
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Colorblind |
Not Colorblind |
Total |
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Male |
7 |
53 |
60 |
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Female |
1 |
39 |
40 |
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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.
Question 29 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.
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Question 30 of 40 |
2.5 Points |
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.
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Area in one tail |
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0.025 |
0.05 |
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Area in two tails |
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Degrees of Freedom n - 1 |
0.05 |
0.10 |
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6 |
2.447 |
1.943 |
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7 |
2.365 |
1.895 |
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8 |
2.306 |
1.860 |
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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. Reset Selection
Question 31 of 40
2.5 Points
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.
Question 32 of 40
2.5 Points
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
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2.5 Points |
The following data were analyzed using one-way analysis of variance.
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B |
C |
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34 |
27 |
19 |
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26 |
23 |
31 |
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31 |
29 |
22 |
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28 |
21 |
22 |
Which one of the following statements is correct?
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A. The purpose of the analysis is to determine whether the groups A, B, and C are independent. |
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B. The purpose of the analysis is to test the hypothesis that the population means of the three groups are equal. |
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C. The purpose of the analysis is to test the hypothesis that the population variances of the three groups are equal. |
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D. The purpose of the analysis is to test the hypothesis that the sample means of the three groups are equal. |
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Question 34 of 40
2.5 Points
A 95% confidence interval for the mean of a normal population is found to be 13.2 < µ < 22.4. What is the margin of error?
A. 4.6 B. 4.4 C. 4.2 D. 5.6
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Question 35 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.
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Colorblind |
Not Colorblind |
Total |
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Male |
7 |
53 |
60 |
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Female |
1 |
39 |
40 |
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Total |
8 |
92 |
100 |
If gender and colorblindness are independent, find the expected values corresponding to the male combination
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
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Question 36 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.
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A. H0: µ = 180; Ha: µ > 180 |
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B. H0: µ > 180; Ha: µ > 180 |
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C. H0: µ < 180; Ha: µ > 180 |
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D. H0: µ = 180; Ha: µ < 180 |
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Question 37 of 40
2.5 Points
The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem 8 had been 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.
Question 39 of 40
2.5 Points
The critical value of χ2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the χ2 statistic in Problem #21 had been 4.613, state your conclusion about the relationship between gender and colorblindness.
A.
Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
B.
Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
C.
Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related.
D.Do not Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related.
Question 40 of 40
2.5 Points
A 95% confidence interval for the mean of a normal population is found to be 17.6 < µ < 23.6. What is the margin of error?
A. 2.0
B. 2.7
C. 3.0
