find the confidence interval

Question

In addition to teachers and administrative staff, schools also have many other employees, including bus drivers, custodians, and cafeteria workers. In Auburn, WA, the average hourly wage is $24.98 for grounds persons, $21.80 for custodians, and $17.66 for assistant cooks.† Suppose that a second school district employs n = 81

 grounds persons who earn an average of $20.55 per hour with a standard deviation of s = $2.85.

 Find a 95% confidence interval for the average hourly wage (in dollars) of grounds persons in school districts similar to this one. (Round your answers to two decimal places.)

Answer 1

The sample size, n=81.

The sample mean hourly wage for grounds persons = $20.55.

The sample standard deviation s=$2.85.

For a 95% confidence interval, alpha=(1-.95)=0.05.

Therefore alpha over 2=0.025

Since population standard deviation is not known, instead we are given the sample standard deviation s, so we will use t statistic.

degrees of freedom, df =(n-1)=(81-1)=80

t-value for (alpha over 2=0.025) and (df=80) from the table= 1.990

The confidence interval formula is x̄ ± t_α/2,(df) *S/√n.

Plug in the values in the above formula, we get the confidence interval as 20.55 ± 0.6302.

Hence, the lower value of confidence interval is=20.55-0.6302=19.9198=$19.92

The upper value of confidence interval is = 20.55+0.6302= 21.1802 = $21.18. (answers are rounded to two decimal place)