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 below summarizes data collected for 90 applicants - 45 men and 45 women:

MaleFemalen4545Mean19.4118.15Std Dev2.5442.832

Find separate 90% confidence intervals for the average number of pegs males and females can correctly place (note: these intervals areone-sampleintervals from previous material!). The appropriate t-critical point for both intervals is t = 1.68.

• The 90% confidence interval for males is: lower limit =, upper limit =
• The 90% confidence interval for females is: lower limit =, upper limit =
• What do these intervals suggest about gender differences in manual agility?
• The individual intervals suggest males place a greater mean number of pegs because most of the interval for this gender is above the interval for females.
• The individual intervals suggest females place a greater mean number of pegs because most of the interval for this gender is above the interval for males.
• The individual intervals suggest no difference in the mean number of pegs placed by males & females because the two intervals overlap.
• The individual intervals suggest males place a greater mean number of pegs because the entire interval for this gender is above the interval for females.
• The individual intervals suggest females place a greater mean number of pegs because the entire interval for this gender is above the interval for males.

The intervals above didn't take into account a comparison between the two genders like a two-sample interval would have. To estimate the mean difference in the number of pegs correctly placed by the two genders, we can use the following formula:(

y

1

y

2

)

t

s

2

1

n

1

+

s

2

2

n

2

(y1-y2)ts12n1+s22n2

• What type of samples were selected if the formula above is used?
• independent samples
• dependent samples
• Calculate the 90% confidence interval using the t-critical point t = 1.663: lower limit =, upper limit =(Round to 4 decimal places.)
• Which of the following conclusions is correct for the interval calculated?
• With 90% confidence, there is no evidence of a difference in the mean number of correctly placed pegs by the two genders.
• With 90% confidence, we estimate the mean number of pegs placed by males is more than the mean placed by females by some amount between the limits calculated above.
• With 90% confidence, we estimate the mean number of pegs placed by females is more than the mean placed by males by some amount between the limits calculated above.