please answer everything and show work wherever it can be shown 4, A sample of 1

Question

please answer everything and show work wherever it can be shown

4, A sample of 16 individuals is selected from a population with = 75. A treatment is administered to the sample. After treatment, M = 82 and s = 8 (1.0 points) a. b. c. Find the 90% confidence interval. Find the 95% confidence interval. What happens to the width of the interval when you increase the level of confidence (the percent confidence)? d. Does the confidence interval include always include the population mean, sample mean, or both?

Explanation / Answer

a) here sample mean M =82

and std error of mean =std deviation/(n)1/2 =8/(16)1/2 =2

for 90% CI and (n-1=15) degree of freedom ; critical value of t =1.753

hence 90% confidence interval for population mean =sample mean -/+ t*Std error =78.4939 to 85.5061

b)

for 95% CI and (n-1=15) degree of freedom ; critical value of t =2.1314

hence 95% confidence interval for population mean =sample mean -/+ t*Std error =77.7371 to 86.2629

c)

as we see that increasing the level ; increases the width of confidence interval.

d)

we can see that confidence interval always contain only sample mean. It gives only confidence to contian population mean but not certainity of containing population mean.

please revert for any explanation/clarification

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