Question

A survey of 30 randomly selected iPhone owners showed that the purchase price has a mean of $600 with a sample standard deviation of $25. (Use z Distribution Table.) Compute the standard error of the sample mean. (Round your answer to the nearest whole number.) Compute the 90% confidence interval for the mean. (Use t Distribution Table.) (Round your answers to 3 decimal places.) To be 90% confident, how large a sample is needed to estimate the population mean within $7? (Round up your answer to the next whole number.)

Answer 1

We have given n = 30, sample mean x bar = 600 , sample standard deviation s = 25

Standard error of sample mean = s / n

= 25 / 30

= 4.56 5

Hence Standard error of sample mean is 5

Sample size n:

We have given C = 90% , E = 7 , = 25

Sample size n = [ (Z_0.90* ) / E ]²

= [ (1.645 * 25) / 7 ]²

= 34.51  

35 (Rounded to the next integer)

Hence the required sample size n = 35

Hope this will help you. Thank you :)