Recitation Practice Problems Week #5 – Autumn 2014 1. According to one survey, Compaq computers hold 8% of the laptop notebook computer market. Suppose Compaq executives believe this figure is too low. To test this, they conduct a survey. Of the two-hundred respondents who own a laptop notebook computer, twenty-four own a Compaq. Answer the following questions assuming a significance level of 0.05 is used. a. Write the hypotheses. b. What is (are) the critical p-hat value(s)? c. What is the value of the test statistic? d. What is the P-value for the test? e. What conclusion do you draw from this test? f. If they use a sample size of 200, what power will their test have to detect that the market share is higher than 8% when it is in fact 12%? g. What sample size is needed to ensure a power of 0.85 when market share is 12% if the significance level remains at 0.05?Recitation Practice Problems Week #5 – Autumn 2014 2. A suitcase is manufactured using a certain strengthening process called Process “A”. Another suitcase equivalent to the first in terms of function and capacity is manufactured using a new strengthening process called Process “B”. Ten overseas tour guides are randomly selected and each is given a suitcase manufactured from each of the two processes. After six months, the manufacturer obtains the opinions from each of the tour guides as to the relative durability of each case, rated on a scale of 1 to 10. The data is shown below. Estimate the average difference in ratings given by the guides for the Process A and Process B suitcases with a 95% confidence interval. Is it reasonable to conclude that the two processes are perceived by the tour guides as producing an equivalent product? Let α = 0.05. Conf. Intervals (Paired-Sample) Process A - Process B Sample Size 10 Sample Mean -0.9 Sample Std Dev 1.595 Confidence Level 95.0% Degrees of Freedom 9 Lower Limit -2.041 Upper Limit 0.241 Guide Process A Process B Di 1 8 9 -1 2 5 7 -2 3 6 6 0 4 2 4 -2 5 5 7 -2 6 5 4 1 7 8 8 0 8 6 8 -2 9 5 3 2 10 4 7 -3 Di Conf. Intervals (One-Sample) Data Set #1 Sample Size 10 Sample Mean -0.900 Sample Std Dev 1.595 Confidence Level (Mean) 95.0% Degrees of Freedom 9 Lower Limit -2.041 Upper Limit 0.241 Q-Q Normal Plot of Difference / Data Set #1-3.5-2.5-1.5-0.50.51.52.53.5-3.5 -2.5 -1.5 -0.5 0.5 1.5 2.5 3.5Z-ValueStandardized Q-ValueRecitation Practice Problems Week #5 – Autumn 2014 3. In testing the hypothesis 100:0H vs. 100:1H, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true? A. The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. B. The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is 0.074 C. The probability that the population mean is larger than 100 is 0.074 D. None of the above 4. We have created a 95% confidence interval for  with the result (8, 13). What decision will we make if we test : 15oH vs. 1: 15H at = 0.05? a. Reject oH in favor of 1H b. Accept oH in favor of 1H c. Fail to reject oH in favor of 1H d. We cannot tell what our decision will be from the information given 5. Refer to question #4. What value of the point estimate for  was used to create this interval? 6. Refer to question #4. With 95% certainty, what is the maximum reasonable sampling error in this interval? 7. If the standard error of the sampling distribution of the sample proportion is 0.0337 for samples of size 200, then the population proportion must be either: A. 0.25 or 0.75 B. 0.20 or 0.80 C. 0.35 or 0.65 D. 0.30 or 0.70 8. A director of marketing research needs a sample of households to participate in the testing of a new toothpaste package. If the target population proportion of households who prefer the new package is 40%, what is the probability that a random sample of 300 households will result in a proportion between 0.35 and 0.45?Recitation Practice Problems Week #5 – Autumn 2014 9. The problem with relying on a point estimate of a population parameter is that: A. it has no variance B. it might be unbiased C. it might not be relatively efficient D. it does not tell us how close or far the point estimate might be from the parameter 10. The width of a confidence interval estimate of the population mean widens when the: A. level of confidence increases B. sample size decreases C. value of the population standard deviation increases D. All of the above 11. A 90% confidence interval estimate of the population mean can be interpreted to mean that: A. if we repeatedly draw samples of the same size from the same population, 90% of the values of the sample means xwill result in a confidence interval that includes the population mean . B. there is a 90% probability that the population mean  will lie between the value of the lower confidence limit (LCL) and the value of the upper confidence limit (UCL). C. we are 90% confident that we have selected a sample whose range of values does not contain the population mean . D. We are 90% confident that 10% the values of the sample means xwill result in a confidence interval that includes the population mean . 12. In developing an interval estimate for a population mean, the population standard deviation was assumed to be 10. The interval estimate was 50.922.14. Had  equaled 20, the interval estimate would be A. 60.92  2.14 B. 50.92  12.14 C. 101.84  4.28 D. 50.92 