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MA260 Statistical Analysis Online Exam 8 Answers (Ashworth College)

11. A skeptical

11. 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. 12. 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. 13. 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. 14. 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. 15. 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. 16. 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: H 0 : µ = 8.0 hours H a : µ > 8.0 hours Explain the meaning of a Type II error. 17. 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. 18. A two-tailed test is conducted at the 0.10 significance level. What is the P-value required to reject the null hypothesis? 19. 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. 20. 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? 21. Which of the following statements is true? 22. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. 23. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X 2 statistic is 4.613, state your conclusion about the relationship between gender and colorblindness. 24. 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? 25. Which of the following statements is true? 26. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X 2 statistic is 3.427, state your conclusion about the relationship between gender and colorblindness. 27. 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.

28. 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. 30. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. ColorblindNot ColorblindTotal Male 7 53 60 Femal 1 39 40 e Total 8 92 100 State the null and alternative hypothesis for the information above. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. ColorblindNot ColorblindTotal Male 8 52 60 Femal 2 38 40 e Total 10 90 100 Find the value of the X 2 statistic for the data above. 31. The __________ test statistic is for the one-way analysis of variance. 32. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The critical value of X 2 for a 2 x 2 table using a 0.05 significance level is 3.841. If the value of the X 2 statistic is 3.179, state your conclusion about the relationship between gender and colorblindness. 34. One hundred people are selected at random and tested for colorblindness to determine whether gender and colorblindness are independent. The following counts were observed. ColorblindNot ColorblindTotal Male 7 53 60 Femal 1 39 40 e Total 8 92 100 Find the value of the X 2 statistic for the data above. 35. 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? 36. 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. 37. 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? 38. 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?