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:
|
Male |
Female |
| n |
45 |
45 |
| Mean |
20.05 |
17.34 |
| Std Dev |
2.708 |
3.65 |
Find separate 90% confidence intervals for the average number of
pegs males and females can correctly place (note:
these intervals are one-sample intervals 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 the interval for this gender is greater than
the interval for females.
- The individual intervals suggest females place a greater mean
number of pegs because the interval for this gender is greater than
the interval for males.
- The individual intervals suggest females place a greater mean
number of pegs because most the interval for this gender is greater
than the interval for males.
- The individual intervals suggest males place a greater mean
number of pegs because most of the interval for this gender is
greater than the interval for females.
- The individual intervals suggest no difference in the mean
number of pegs placed by males & females because the two
intervals overlap.
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:
(¯y1−¯y2)±t√s21n1+s22n2(y¯1-y¯2)±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 = 1.664: lower limit = , upper limit =
(Round to 4 decimal places.)
- Which of the following conclusions is correct for the interval
calculated?
- 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.
- With 90% confidence, there is no evidence of a difference in
the mean number of correctly placed pegs by the two genders.