core: 3.33 of 6 pts 14 of 1 7 (14 complete) Score: 64.71 %, 64.71 a 9.2.19 Quest

Question

core: 3.33 of 6 pts 14 of 1 7 (14 complete) Score: 64.71 %, 64.71 a 9.2.19 Question Help A simple random sample of size n is drawn. The sample mean, x, is found to be 17.9, and the sample standard deviation, s, is found to be 4.2 Click the icon to view the table of areas under the t-distribution. (a) Construct a 95% confidence interval about if the sample size, n, is 34. Lower bound: 16.43: Upper bound: 19.37 (Use ascending order. Round to two decimal places as needed.) (b) Construct a 95% confidence interval about if the sample size, n, is 51. Lower bound: 16.72; Upper bound: 19.08 (Use ascending order. Round to two decimal places as needed.) How does increasing the sample size affect the margin of error, E? O A. The margin of error does not change. O B. The margin of error ioreases. C. The margin of error decreases (c) Construct a 99% confidence interval about if the sample size, n, is 34. Lower bound: Upper bound: (Use ascending order. Round to two decimal places as needed.) Enter your answer in the edit fields and then click Check Answer Clear All

Explanation / Answer

we know that the confidence interval is given as
mean +- MOE , where

MOE = z*sd/sqrt(n)

here z = 2.58 for 99% CI from the z table
putting the values

n = 34
sd = 4.2
mean = 17.9

putting the values and solving we get

17.9 +- 2.58*4.2/sqrt(34), solving for the plus and the minus sign we get

16.04,19.75

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