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

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

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

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

Answer 1

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

option A is true

2 ) using excel we have

Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation	1600
Sample Mean	45000
Sample Size	9
Confidence Level	95%
Intermediate Calculations
Standard Error of the Mean	533.3333333
Degrees of Freedom	8
t Value	2.306004135
Interval Half Width	1229.868872
Confidence Interval
Interval Lower Limit	43770.13
Interval Upper Limit	46229.87

\ a 95% confidence interval to estimate the mean salary is given by option c

option a is true 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 shorter than the interval in the previous problem.