The random sample shown below was selected from a normal distribution. Complete
ID: 3335501 • Letter: T
Question
The random sample shown below was selected from a normal distribution. Complete parts a and b. a. Construct a 90% confidence interval for the population mean . Round to two decimal places as needed) b. Assume that sample mean x and sample standard deviaton s remain exactly the same as those you just calculated but thet are based on a sample of n-25 observations. Repeat pert a. What is the effect of increasing the sample s ze on the width of the confidence ntervals? The confidence interval is. (Round to two decimal places as needed.) What is the effect of the sample size on the width of the confdence interval? O A. As the sample size increases, the width stays the same. O B. As the sample size increases, the width increases. O C. As the sample size increases, the width decreases.Explanation / Answer
3,4,4,6,10,9
a. Sample mean x' = (3 + 4 + 4 + 6 + 10 + 9) / 6
= 6
Sum of squares of differences SS = (3-6)*(3-6) + (4-6)*(4-6) + (4-6)*(4-6) + (6-6)*(6-6) + (10-6)*(10-6) + (9-6)*(9-6)
= 42
Sample Variance s2 = 42 / 5 = 8.4
Sample standard deviation s = 2.8983
n = 6 z for 90% is 1.645
(a,b) = x' +/- zs / n
= 6 +/- 1.645*2.8983/6
= (4.05, 7.95)
b. n = 25
(a,b) = x' +/- zs / n
= 6 +/- 1.645*2.8983/25
= (5.05, 6.95)
A. As the sample size increases, the width decreases.