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  1. STATISTICAL TECHNIQUES IN BUSINESS & ECONOMICS
  2. Chapter 9: Estimation and Confidence Intervals

9.1 Introduction

PreviousChapter 9: Estimation and Confidence IntervalsNextChapter 10: One-Sample Tests of Hypothesis

Last updated 1 year ago

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

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

Formula of standard error of sample mean