Question

1.) Assume that a sample is used to estimate a population mean μμ. Find the 95% confidence interval for a sample of size 700 with a mean of 55.8 and a standard deviation of 14.1. Enter your answer as a tri-linear inequality accurate to 4 decimal places.
< μ <

2.) Assume that a sample is used to estimate a population mean μμ. Find the 99% confidence interval for a sample of size 69 with a mean of 58.1 and a standard deviation of 21.9. Enter your answer as an open-interval (i.e., (Low, High)) reported to 4 decimals.

99% C.I. =  

The answer should be obtained without any preliminary rounding.

Answer 1

1) The statistical software output for this problem is:

One sample T summary confidence interval:
μ : Mean of population

95% confidence interval results:

Mean	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
μ	55.8	0.53292991	699	54.753665	56.846335

Hence,

95% confidence interval will be:

54.7537 < μ < 56.8463

2) The statistical software output for this problem is:

One sample T summary confidence interval:
μ : Mean of population

99% confidence interval results:

Mean	Sample Mean	Std. Err.	DF	L. Limit	U. Limit
μ	58.1	2.6364502	68	51.113193	65.086807

Hence,

99% CI = (51.1132, 65.0868)