# Confidence Interval

1)

a statistian claims that the average score on a test of students for students who major in psychology is greater than that of

students who major in math results given to 50 students in each group are shown here Is there enough evidence to support the statisticians claim at @=0.01 Show work.

Physc Math

X1=118 X2=115

@1=15 @2=15

n1=50 n2=50

2)

2 brands of batteries are tested and their voltage compared The data

follow Find the 95% confidence interval of the true difference of the

mean Assume that both variables are normally distributed Show all the work

Brand x Brand Y

X1=9.2volts X2=88volts

@1=0.3volts @2=01volts

n1=27 n2=30

3)

A reseacher suggest that male nurses earn more than female nurses. A

survey of 16 male nurses and 20 female nurses reports the following data.

Is there enough evidence to support the claim that male nurses earn

more than female nurses. Use @=0.05 Show all the work

Male Female

X1=$23,800 X2=$23,750

s1=$300 s2=$250

n1=16 n2=20

#### Solution Preview

please refer to the attachment.

the formula for a confidence interval on the difference between means ( M1 - M2) is:

Md (t)( )

where Md = M1 - M2 is the statistic and is an estimate of (the standard error of the difference between means). t depends on the level of confidence desired and on the degrees of freedom. The estimated standard error, , is computed assuming that the variances in the two populations are equal. If the two sample sizes are equal (n1 = n2) then the population variance 2 (it is the same in both populations) is estimated by using the following formula:

MSE = ( )/2

where MSE (which stands for mean square error) is an estimate of sigma2. Once MSE is calculated, can be computed as follows:

=

1) H0: M1=M2 or M1-M2=0 vs H1: M1>M2

The first step is to compute the means of each group: M1 = 118 and M2 = 115.

Therefore, Md = 118 - 115 = 3.

= 15^2=225 and = 225.

MSE = (225 + 225)/2 =225. From the formula:

= = SQRT(2*225/2) = 15

We can calculate the t-stat for Md is td= (Md-0)/ ...

#### Solution Summary

The solution addresses - 1) a statistician claims that the average score on a test of students for students who major in psychology is greater than that of students who major in math results given to 50 students in each group are shown here Is there enough evidence to support the statisticians claim at @=0.01.