statistics exam 8
sarkha1
statistics_exam_8.docx|
Question 1 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?
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A. 1.12 |
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B. 1.48 |
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C. 1.84 |
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D. 2.15 |
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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 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.
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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.
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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. |
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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. |
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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. |
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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. |
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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.
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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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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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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.
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A. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported. |
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B. Do not reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported. |
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C. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months is supported. |
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D. Reject the null hypothesis and conclude that the claim that the mean is different from 18.7 months cannot be supported. |
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Question 12 of 40 |
2.5 Points |
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.
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A. Ho: µ = 9.3 minutes H : µ < 9.3 minutes |
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B. Ho: µ = 9.3 minutes H : µ > 9.3 minutes |
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C. Ho: µ = 9.3 minutes H : µ 9.3 minutes |
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D. Ho: µ 9.3 minutes H : µ = 9.3 minutes |
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A two-tailed test is conducted at the 5% significance level. What is the P-value required to reject the null hypothesis?
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Question 14 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.
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A. Reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats. |
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B. Do not reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats. |
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C. Reject the null hypothesis. Conclude that there is sufficient evidence that more than half of all voters prefer Democrats. |
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D. Do not reject the null hypothesis. Conclude that there is insufficient evidence that more than half of all voters prefer Democrats. |
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Question 15 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.
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A. Conclusion: Support the claim that the mean is equal to 16 ounces. |
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B. Conclusion: Support the claim that the mean is greater than 16 ounces. |
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C. Conclusion: Support the claim that the mean is not equal to 16 ounces. |
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D. Conclusion: Support the claim that the mean is less than 16 ounces. |
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Question 16 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.
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A. Conclusion: Support the claim that the mean is less than 9.4 minutes. |
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B. Conclusion: Support the claim that the mean is greater than 9.4 minutes. |
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C. Conclusion: Support the claim that the mean is equal to 9.4 minutes. |
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D. Conclusion: Do not support the claim that the mean is greater than 9.4 minutes. |
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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.
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without computing a P-value, determine whether the alternate hypothesis is supported and give a reason for your conclusion.
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z = 1.8 for Ha: µ > claimed value. What is the P-value for the test?
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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 = 0.9 ounces.
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One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
State the null and alternative hypothesis for the information above.
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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. State the null and alternative hypotheses for this test.
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2.5 Points |
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.
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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 |
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A. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 160 yards. |
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B. Reject the null hypothesis. The data does provide sufficient evidence that the average distance is greater than 160 yards. |
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C. t= 1.2334; Critical value = 1.992 |
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D. Insufficient information to answer this question. |
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One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
Find the value of the χ2 statistic for the data above.
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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?
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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 |
State the null and alternative hypothesis for the test associated with this data.
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A. H0: Colorblindness and gender are dependent characteristics. Ha: Colorblindness and gender are not related in any way. |
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B. H0: Colorblindness and gender are dependent characteristics. Ha: Colorblindness and gender are related in some way. |
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C. H0: Colorblindness and gender are independent characteristics. Ha: Colorblindness and gender are not related in any way. |
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D. H0: Colorblindness and gender are independent characteristics. Ha: Colorblindness and gender are related in some way. |
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The __________ test statistic is for the one-way analysis of variance.
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Question 28 of 40 |
2.5 Points |
Which of the following statements is true?
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A. The t distribution can be used when finding a confidence interval for the population mean whenever the sample size is small. |
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B. The p distribution can be used when finding a confidence interval for the population mean whenever the sample size is small. |
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C. The t distribution cannot be used when finding a confidence interval for the population mean whenever the sample size is small. |
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D. The p distribution cannot be used when finding a confidence interval for the sample mean whenever the sample size is small. |
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Question 29 of 40 |
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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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.
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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?
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One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed.
If gender and colorblindness are independent, find the expected values corresponding to the male combinations of gender and colorblindness.
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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.
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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.
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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.
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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.
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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 |
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.
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Colorblind |
Not Colorblind |
Total |
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Male |
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Female |
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Total |
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A. Male Colorblind 6.0; Male Not Colorblind 54.0 |
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B. Male Colorblind 7.0; Male Not Colorblind 53.0 |
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C. Male Colorblind 8.0; Male Not Colorblind 52.0 |
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D. Male Colorblind 6.0; Male Not Colorblind 53.0 |
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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.
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A. Do not reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related. |
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B. Do not reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related. |
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C. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related. |
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D. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related. |
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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 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.
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