6. You have measured the systolic blood pressure of a random sample of 25 employ
ID: 2936548 • Letter: 6
Question
6. You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of the confidence level? a. 95% of the sample of employees have a systolic blood pressure between 122 and 138. b. 95% of the population of employees have a systolic blood pressure between 122 and 138. c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure. d. The probability that the population mean blood pressure is between 122 and 138 is .95.
7. If the 98% confidence limits for the population mean are 73 and 80, which of the following could be the 95% confidence limits? a. 73 and 81 b. 72 and 79 c. 72 and 81 d. 74 and 79
8. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct? a. The intervals have the same width. b. The 99% interval is longer. c. The 99% interval is shorter. d. None of the above.
9. Which of the following confidence intervals will be the smallest? a. 80% b. 95% c. 90% d. 98%
10. Which of the following best describes the shape of the sampling distribution of the sample proportion?
a. When standardized, it is exactly the standard normal distribution.
b. When standardized, it is the t distribution.
c. It is approximately normal as long as n 30.
d. It is approximately normal as long as np 10 and n(1-p) 10.
Explanation / Answer
6. Note that the confidence interval is for a parameter and hence is used to estimate population mean.
The correct answer is c.If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean.
7. If the confidence level is decreased, the confidence interval gets broader. Since the values for 98% are 73 and 80, the only possible value for 95% is 72 and 81 among the four.
The correct answer is c.
8. Since the confidence level is increased, c. The 99% interval is shorter
9. As noted in the two problems above, the smallest confidence interval corresponds to the biggest confidence level i.e d. 98%.
10. The shape of the sampling distribution of the sample proportion is:
d. It is approximately normal as long as np 10 and n(1-p) 10.
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