Question

An auditing firm is interested in estimating the mean cost out pocket of uniform/work clothing for employes in the US. They survey SRS of 100 individuals who buy their own work clothing and find that x = 168 and s, = 21 (in USD). (a) State the parameter our confidence interval will estimate. (b) Identify the conditions that must be met to use this procedure, and explain how you know that each one has been satisfied. (c) Find the appropriate critical value and the standard error of the sample proportion. (d) Give the 95% confidence interval. (e) Interpret the confidence interval constructed in part D. in the context of the problem.

Answer 1

Answer:

n= 100, $\bar x$ =168, s= 21

a)

We want to estmate the

Population mean ($\mu$) cost of uniform for employees in the US

b)

conditins for confidence interval are as follows

i) sample data should be drawn from normaly distributed population

or sample should be large or at least 30

ii) sample should be random.

here both conditions are met.

c)

now find t critical value for c= 95% with df= n-1 = 99

using t table we get

t critical value = 1.984

formula to calculate standard error is

$= \frac{s}{\sqrt{n}}$

$= \frac{21}{\sqrt{100}} = 2.1$

Standard error = 2.1

d)

formula for confidence interval is

1 tc*

$168 \pm 1.984 * \frac{21}{\sqrt{100}}$

168−4.167 < $\mu$ < 168+4.167

163.833 < $\mu$ <  172.167

( 163.833 , 172.167)

thus we get confidence interval as ( 163.833 , 172.167)

e)

We are 95% confident that the true population mean cost of uniform of employees in the US lies between 163.833 USD to 172.167 USD.