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Question 3 of 16 (15 points) I Attempt 1 of 1 View question in a popup | 卤 2h 28m Remaining 7.1 Section Exercise 39-40 A population has standard deviation 17.4. alo Part 1 of 2 (a) How large a sample must be drawn so that a 95% confidence interval for μ will have a margin of error equal to 4.2? Round the answer up to the nearest integer. (Round the critical value to no less than three decimal places.) A sample size of | | is needed to be drawn in order to obtain a 95% confidence interval with a margin of error equal to 4.2. Part 2 of 2 (b) If the required confidence level were 90%, would the necessary sample size be larger or smaller? (Choose one) ,because the confidence level is (Choose one)

Answer 1

Solution: a) Given that, σ-17.4.5-4.2 Critical value: Using the z-table, the critical value at 5% level of significance for a two tailed t .960 test is 001 The sample size is calculated as follows: -0.056 26 1.960x17.4 4.2 65.932 66 (round up to next integer) Thus, the approximate sample size is 66.

b) Given that. 17.4. E-42 Critical value: Using the z-table, the critical value at 10% level of significance for a two tailed test is 01.645 The sample size is calculated as follows: 1.645 x17.4 4.2 46.436 47 (round up to next integer) Thus, the approximate sample size is 47. The sample size is smaller because the confidence level is decrease.