Question

A study based on a random sample of 17 reported a sample mean of 65 with...

A study based on a random sample of 17 reported a sample mean of 65 with a sample standard deviation of 4.

1. Calculate a 95% Confidence interval.
1. What is the margin of error?

1. If we calculated a 90% confidence interval, as compared to your answer in part b, would your margin of error increase: (choose one)

1. increase
2. decrease
3. stay the same

1. If we increase the sample size to 50 persons, but the reported sample mean and sample standard deviation stayed the same as in part a, would the 95% confidence interval get: (choose one)

1. wider
2. narrower
3. stay the same

1)

 sample mean 'x̄= 65 sample size   n= 17 sample std deviation s= 4 std error 'sx=s/√n= 0.9701
 for 95% CI; and 16 df, value of t= 2.120 margin of error E=t*std error    = 2.057 lower bound=sample mean-E = 62.9434 Upper bound=sample mean+E = 67.0566 from above 95% confidence interval for population mean =(62.94,67.06)

2)

margin of error =2.057 ~ 2.06

3)margin of error

decrease

4)

95% confidence interval get narrower