Statistical Analysis and Confidence Interval Estimation Guide

Extra Review. Question Block 1: In rural areas, newspaper carriers deliver morning papers using their cars because the length of the route makes it hard to walk. In a random sample of 31 carriers who use their cars, the sample mean route length was 16.7 miles with a sample standard deviation of 3.4 miles. Assume all assumptions needed are met, construct a 99% confidence interval estimate for the population mean route length for newspaper carriers in a rural area. a. What type of variable are we studying? b. Give the point estimate (round to one decimal place). c. Give the critical value (round to four decimal places) d. Give the standard error (round to two decimal places) e. State the margin of error (round to two decimal places) f. Calculate the confidence interval. (round to two decimal places). g. Interpret the interval in question f as we have done in lecture. h. What is the likelihood that our confidence interval does not contain the true population mean? i. State two ways to make the confidence interval narrower.

Question Block 2: A US textile company is interested in the proportion of orders shipped to another country. In a random sample of 1560 clothing orders placed 468 were shipped to another country. Construct a 90% confidence interval estimate for the population proportion of clothing orders shipped to another country. a. What is the confidence interval estimating? b. Give the point estimate (round to two decimal places) c. Give the critical value (round to two decimal places) d. Give the standard error (round to two decimal places) e. State the margin of error (round to two decimal places) f. Calculate the confidence interval. (round to two decimal places) g. State two ways to make the confidence interval wider.

Question Block 3: Homeschooling has become very popular in the United States, and many colleges try to attract students from this group. Evidence suggests that approximately 90% of all homeschooled children attend college. A random sample of 225 homeschooled children was obtained, and 189 of them were found to have attended college. Is there evidence that the population proportion of homeschooled children who attend college is different than 90%. Use a level of significance of 0.05. a. State the correct hypotheses (using the notation covered in lecture). H 0 : H a : b. Calculate the appropriate test statistic (round to two decimal places) c. Calculate the appropriate p-value (round to four decimal places) d. State your decision. e. Interpret the results in the way we did in lecture.

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Question Block 4 According to a recent study, the attention span of an adult has decreased from the mean of 12 seconds found in 2000. A random sample of 18 adults was obtained and the attention span of each was measured using a standardized test. The sample had a sample mean of 10.85 seconds with a standard deviation of 2.1 seconds. Is there any evidence to suggest that the true population mean attention span is less than 12 seconds? Assume the underlying distribution is normal and use a level of significance of 0.01. The following output from was created: Sample mean = 10.85. Test Statistic = -2.32. Standard error = 0.49497. p-value = 0.0164 a. What type of variable is being studied? b. What type of test is being performed? c. Which result given describes the number of standard errors between the sample statistic and the hypothesized value? d. Which result given describes the probability of getting the sample result or one less than it if the true population mean was 12? e. What is the correct decision for the hypothesis test? f. What was the assumed true value of the population parameter when the test statistic was calculated?

Question Block 5: A study was done to determine if there is a difference in the population mean airspeeds of two types of leaf blowers: a Craftsman leaf blower and an Echo leaf blower. Assume the underlying distributions are normal. Is there any evidence to suggest that the population mean airspeeds are different? Use a level of significance of 0.05. Use the provided output to help perform the test. Note: μ 1 =population mean airspeed of Craftsman. μ 2 =population mean airspeed of Echo Hypothesis test results: Test Statistic = 1.83 P-value = 0.0765 95% Confidence Interval estimate for μ 1 − μ 2 : (-1.72, 32.28) a. Identify if these populations are dependent or independent and justify your answer. b. What type of test is being done? Paired-t or two-sample t c. State the hypothesis (in the correct notation). d. What is the conclusion of the hypothesis test? Include decision and interpretation. e. Based on the confidence interval is there evidence of a difference in the airspeeds? Justify your answer and if one of the groups always has a higher mean state which group.

Extra Review Exam 3 (3)

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