A factory hiring people to work on an assembly line gives job applicants a test of manual agility. This test counts how many strangely shaped pegs the applicant can fit into matching holes in aone-minute period. The table to the right summaries the data by gender of the job applicant. Assume that all conditions necessary for inference are met. Complete parts a through f.

Male

Female

Number of subjects

45

45

Pegsplaced:

Mean

19.44

17.17

SD

2.65

3.71

a) Find 98% confidence intervals for the average number of pegs that males and females can each place.

The 98% confidence interval for males is (

nothing

,

nothing

).

(Round to two decimal places asneeded.)

The 98% confidence interval for females is (

nothing

,

nothing

).

(Round to two decimal places asneeded.)

b) If those intervalsoverlap, what does this suggest about anygender-based difference in manualagility?

A.

The intervals do not overlap.

B.

It may appear to suggest that there is a difference in the mean number of pegs placed by males andfemales, but atwo-sample t-interval should be constructed to assess the difference in mean number of pegs placed.

C.

It may appear to suggest that there is no difference in the mean number of pegs placed by males andfemales, but atwo-sample t-interval should be constructed to assess the difference in mean number of pegs placed.

c) Find a 98% confidence interval for the difference in the mean number of pegs that could be placed by men and women.

The 98% confidence interval for the difference menwomen is (

nothing

,

nothing

).

(Round to two decimal places asneeded.)

d) What does this interval suggest about anygender-based difference in manualagility?

A.

With 98% confidence, there is no difference in the mean number of pegs placed by males and females.

B.

With 98% confidence, the mean number of pegs placed by females is greater than the mean number of pegs placed by males by an amount in the interval.

C.

With 98% confidence, the mean number of pegs placed by males is greater than the mean number of pegs placed by females by an amount in the interval.

e) The two results seem contradictory. Which method iscorrect: doingtwo-sample inference, or doingone-sample inferencetwice?

one-sample inference twice

two-sample inference

f) Whydon't the resultsagree?

A.

Using two different confidence intervals adds the variances instead of the standard deviations. Thetwo-sample difference of means procedure takes this into account.

B.

Thetwo-sample difference of means procedure adds the standard deviations instead of the variances. Using two different confidence intervals takes this into account.

C.

Using two different confidence intervals adds the standard deviations instead of the variances. Thetwo-sample difference of means procedure takes this into account.

D.

Thetwo-sample difference of means procedure adds the variances instead of the standard deviations. Using two different confidence intervals takes this into account.