1 answer

A manager of a technology start-up company wishes to estimate monthly expenses using a 98% confidence...

Question:

a manager of a technology start-up company wishes to estimate monthly expenses using a 98% confidence interval. she collected a random sample of 60 months and calculated average expenses of $2684 per month. assume σ=8 is known. what is the 98% confidence interval of the average monthly expense?


Answers

Given that, sample size ( n ) = 60

sample mean (ar x) = $2684

population standard deviation (sigma) = 8

A 98% confidence level has significance level (alpha) = 0.02 and critical value is, %2 = 2.33

98% confidence interval for population mean (mu) is,

ar x - Z_{alpha/2} * rac {sigma}{sqrt { n }} < mu < ar x + Z_{alpha/2} * rac {sigma}{sqrt { n }}

2684 - 2.33* -< μ < 2684 V60 2.33 * 石 V60

2684-2.41 < μ < 2684 +2.41

2681.59 < μ < 2686.41

$2681.59 < μ < $2686.41

Therefore, the 98% confidence interval of the average monthly expense is between $2681.59 to $2686.41

.

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