Question

1. Use the following information for the next four problems. A researcher is interested in estimating the mean salary of public school teachers in a particular region. A random sample of 9 teachers is selected and the salary of each one is recorded. The researcher calculates a sample mean of $45,000 and a sample standard deviation of $1,600. Assume that the salaries in the population vary according to a normal distribution.

   The mean salary of all public school teachers in the region is a __________ while the sample mean $45,000 is a __________.

   	a.	statistic, parameter
   	b.	parameter, parameter
   	c.	statistic, statistic
   	d.	parameter, statistic

2. Calculate a 95% confidence interval to estimate the mean salary.

   	a.	$45,000  $1,045.33
   	b.	$45,000  $348.44
   	c.	$45,000  $1,206.40
   	d.	$45,000  $1,229.87

3. Suppose, instead, that a larger sample of teachers had been selected while still using the 95% confidence level. The new confidence interval, based on the larger sample, would be __________ the interval in the previous problem.

   	a.	the same length as
   	b.	longer than
   	c.	shorter than

4. For this problem only, suppose that the confidence interval above had ranged from $43,500 to $46,500. Which one of the following would give a correct interpretation of the confidence interval?

   	a.	95% of all public school teachers in the region earn between $43,500 and $46,500.
   	b.	95% of the public school teachers in the sample earn between $43,500 and $46,500.
   	c.	We are 95% confident that the mean salary of the public school teachers in the sample is between $43,500 and $46,500.
   	d.	We are 95% confident that the mean salary of all public school teachers in the region is between $43,500 and $46,500.

Answer 1

1) option D parameter, statistic

2)

sample mean 'x̄=	45000.000
sample size   n=	9.00
sample std deviation s=	1600.000
std error 'sx=s/√n=	533.333

for 95% CI; and 8 df, value of t=		2.306
margin of error E=t*std error    =		1229.867
lower bound=sample mean-E =		43770.133
Upper bound=sample mean+E =		46229.867
from above 95% confidence interval for population mean =(43770.13,46229.87)

option D $45,000-/ + $1,229.87

3)

shorter than

4)

option D

We are 95% confident that the mean salary of all public school teachers in the region is between $43,500 and $46,500.