Statistics-Final
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questions_to_stats_final.docxA two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis?
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A. Greater than or equal to .010 |
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B. Greater than or equal to 0.05 |
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C. Less than or equal to 0.10 |
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D. Less than or equal to 0.05 |
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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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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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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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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.
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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. |
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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. |
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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. |
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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.
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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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A.
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B.
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C.
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D. is more than 4 standard deviations above the claimed mean |
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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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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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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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A. Smaller. E decreases as the square root of the sample size gets larger. |
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B. Smaller. E increases as the square root of the sample size gets larger. |
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C. Larger. E decreases as the square root of the sample size gets larger. |
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D. Larger. E increases as the square root of the sample size gets larger |
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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.
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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 X2 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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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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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 4.613, state your conclusion about the relationship between gender and colorblindness.
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A. Reject H0. There is not sufficient evidence to support the claim that gender and colorblindness are related. |
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B. Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related. |
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C. Do not Reject H0. There is sufficient evidence to support the claim that gender and colorblindness are related. |
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D. Do not Reject H0. There is not 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.
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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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. Reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards. |
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B. Reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards. |
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C. Do not reject the null hypothesis. The data do provide sufficient evidence that the average distance is greater than 180 yards. |
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D. Do not reject the null hypothesis. The data do not provide sufficient evidence that the average distance is greater than 180 yards.
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.
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.
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 25 and the sample standard deviation did not change, would the margin of error be larger or smaller than 9.3?
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 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?
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Which of the following statements is true?
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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. |
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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. |
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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. |
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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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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.
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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 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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A. 4.4 |
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B. 4.6 |
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C. 4.8 |
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D. 5.0 |
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