Question

14a. Suppose we know that σ=10 but we do not know µ. We would like to specify the interval that with 95% confidence contains µ. The data are Xi: 10, 30, 20, 25. Determine this confidence interval. 14b. Suppose we know that σ=10 but we do not know µ. We would like to specify the interval that with 95% confidence contains µ. The data are Xi: 15, 20, 10, 30, 17, 24, 21, 15. Determine this confidence interval. 14c. Is the confidence interval in Exercise 14b narrower or wider than the one in Exercise 14a? Explain why.

Answer 1

Suppose we know that σ=10 but we do not know µ. We would like to specify the interval that with 95% confidence contains µ. The data are Xi: 10, 30, 20, 25. Determine this confidence interval.

	CI
Sample Size	4
Sample Mean	21.25
Standard Deviation	10.00
Confidence Coefficient	0.95
Significant level	0.05
Margin of error	9.80
Point Estimate	21.25
Lower Limit	11.45
Upper Limit	31.05

(95 % confidence interval is - (11.45, 31.05)

14b. Suppose we know that σ=10 but we do not know µ. We would like to specify the interval that with 95% confidence contains µ. The data are Xi: 15, 20, 10, 30, 17, 24, 21, 15. Determine this confidence interval.

	CI
Sample Size	8
Sample Mean	19.00
Standard Deviation	10.00
Confidence Coefficient	0.95
Significant level	0.05
Margin of error	6.93
Point Estimate	19.00
Lower Limit	12.07
Upper Limit	25.93

(95 % confidence interval is (12.07, 25.93)

Formula to calculate the Confidence interval.

Sample size is the thotal Xi value count: sample size is 4. Sample mean (mu) is nothing but average value of XI(data set)

formula to find XI is "=Average(A1:A4)"

Standard deviation as given as 10.

Is the confidence interval in Exercise 14b narrower or wider than the one in Exercise 14a? Explain why.

14 B is narrower than the exercise 14A. because upper limit value is lesser than the 14 a.

Formula reference: