I need help with this question The book is Basic Statistics

I need help with this question. The book is Basic Statistics for Business & Economics 8 E.

A recent study of 34 Summerdale, Pennsylvania residents revealed they had lived at their current address for a mean of 8.6 years, with a sample standard deviation of 2 years.

[a] What is the population mean?

[b] What is the best estimate of the population mean?

[c] The standard error of the mean is 0.343. How did I find that answer? *Show me your work to find the answer.*

[d] Develop a 90% confidence interval for the population mean. *Use Appendix B.2 and round your answer to the nearest hundredth.*

Solution

a)

We cannot possibly know, but we have a sample mean, the best estimate of the population mean.

b)

The best estimate is the sample mean, 8.6 years. [answer]

c)

standard error = s / sqrt(n) = 2/ sqrt(34) = 0.343 [answer]

d)

a)

We cannot possibly know, but we have a sample mean, the best estimate of the population mean.

b)

The best estimate is the sample mean, 8.6 years. [answer]

c)

standard error = s / sqrt(n) = 2/ sqrt(34) = 0.343 [answer]

d)

Note that              
              
Lower Bound = X - z(alpha/2) * s / sqrt(n)              
Upper Bound = X + z(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    8.6          
z(alpha/2) = critical z for the confidence interval =    1.645          
s = sample standard deviation =    2          
n = sample size =    34          
              
Thus,              
              
Lower bound =    8.035769655          
Upper bound =    9.164230345          
              
Thus, the confidence interval is              
              
(   8.04   ,   9.16   ) [ANSWER]