# Question: A factory hiring people to work on an assembly line

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 a one-minute period. The table summarizes the data by gender of the job applicant. Assume that all conditions necessary for inference are met.
a) Find 95% confidence intervals for the average number of pegs that males and females can each place.
b) Those intervals overlap. What does this suggest about any gender-based difference in manual agility?
c) Find a 95% confidence interval for the difference in the mean number of pegs that could be placed by men and women.
d) What does this interval suggest about any gender-based difference in manual agility?
e) The two results seem contradictory. Which method is correct: doing two-sample inference, or doing one-sample inference twice?
f) Why don’t the results agree?

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