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 20.17 19.02 Std Dev 2.388 2.712 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
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
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 |
| 20.17 | 19.02 | |
| Std Dev | 2.388 | 2.712 |
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 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 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 most of the interval for this gender is greater than the interval for females.
- 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 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 = 1.663: 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 females is more than the mean placed by males by some amount between the limits calculated above.
- 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, there is no evidence of a difference in the mean number of correctly placed pegs by the two genders.
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