9.1 Introduction

Exercise:

1. A survey of 35 randomly selected “iPhone” owners showed that the purchase price has a mean of $520 with a sample standard deviation of $110.

   a. Compute the standard error of sample mean.

   b. Compute 95 percent confidence interval for mean.

   c. How large of sample size is need to estimate population mean within margin of error $20?

Solution:

Let see the formula

Formula of standard error of sample mean

Based on what we have in the topics:

• s = 110

• n = 35

💡 a. So, SE = 110/√35 = 18.61

💡 b. Compute 95 percent confidence interval for mean

Note: This is formula has been used when we know the standard deviation of population, but now we only know sample standard deviation: 110$, then the formula we used:

What about t value?

let take a look of student's t distribution, when degree of freedom is 34, ( n -1 )

t = 2.032 ==> CI = 520 +-2.032 * 18.6

💡c. Compute sample size when margin of error is $20