SOLUTION: A random sample of 22 people employed by the Florida state authority established they earned an average wage (including benefits) of $61.00 per hour. The sample standard deviation

Question 1091936: A random sample of 22 people employed by the Florida state authority established they earned an average wage (including benefits) of $61.00 per hour. The sample standard deviation was $5.66 per hour. (Use t Distribution Table.)

a. What is the best estimate of the population mean?

Estimated population mean $

b.
Develop a 98% confidence interval for the population mean wage (including benefits) for these employees. (Round your answers to 2 decimal places.)

Confidence interval for the population mean wage is between
and
.

c.
How large a sample is needed to assess the population mean with an allowable error of $1.00 at 95% confidence? (Round up your answer to the next whole number.)

Sample size

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The best estimate of the population mean is $61, the sample mean.
98% CI is 61+/-t df=21,0.99*5.66/sqrt(22); the t is 2.52
the half interval is 3.04, 2.52*5.66/sqrt(22)
the 98% CI is ($57.96, $63.04)
use a z since we don't know the t for the sample size. Then check to see if this works.
half-interval is 1
z*5.66/sqrt(n)=1, and z is 1.96, so
1.96*5.66=sqrt (n)
sqrt(n)=11.09
n=123.06 or 124
check to see if this works for t. It is a little large at 1.006 half interval or (58.994, 61.006)
if one uses 125, it is +/-1.002.
n=126 gives an error of +/-0.998

RELATED QUESTIONS
A random sample of 22 people employed by the Florida state authority established they... (answered by ewatrrr)

A random sample of 22 people employed by the Florida state authority established they... (answered by Boreal)

A random sample of 23 people employed by the Florida state authority established they... (answered by ewatrrr)

help please!! A random sample of 31 people employed by the Florida state authority... (answered by ewatrrr)

Another Question , Help Please A survey of 20 randomly sampled judges employed by the (answered by stanbon,rothauserc)

A local county has an unemployment rate of 8%. A random sample of 19 employable people... (answered by ikleyn)

A local county has an unemployment rate of 4.7%. A random sample of 17 employable people... (answered by ikleyn)

For wages less than the maximum taxable wage base, Social Security contributions... (answered by psbhowmick)

For wages less than the maximum taxable wage base, Social Security contributions... (answered by Theo)