## 14 Apr If the 98% confidence limits for the population

# If the 98% confidence limits for the population

Subject: Mathematics / Statistics

Question

Multiple Choice and work the problem out if necessary

8. 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

e. none of these

9. 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.

10. Which of the following confidence intervals will be the smallest?

a. 80%

b. 95%

c. 90%

d. 98%

11. 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.

e. None of these are correct.

Use the following information to answer questions 12 – 15: A new brand of chocolate bar is being market tested. Five hundred of the new chocolate bars were given to consumers to try. The consumers were asked whether they liked or disliked the chocolate bar. You are given their responses below.

Response Frequency

Liked

Disliked 235

265

Total 500

12. What is the point estimate for the proportion of people who liked the chocolate bar?

a. 235

b. 0.47

c. 0.53

d. 0.95

e. none of these above

13. What is the standard error for the proportion of people who liked the chocolate bar?

a. 0.47

b. 0.53

c. 0.02232

d. 0.0005

e. 0.95

14. If we are to determine a 95% confidence interval for the true proportion of people who liked the chocolate bar, what is the margin of error?

a. 0.47

b. 0.02232

c. 0.0212

d. 0.04375

e. 0.00098

15. Give the 95% confidence interval (a range of values) for the true proportion of people who liked the chocolate bar.

a. [0.4262528, 0.5137472 ]

b. [0.4862528, 0.5737472 ]

c. [-1.489964, 2.429964 ]

d. [0.4691805, 0.4708195 ]

e. none of these above

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