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Population mean tests and hypothesis tests

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Problem #1

Independent random samples of 36 and 50 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here:

Sample 1 Sample 2
Sample Size 36 50
Sample Mean 1.28 1.35
Sample Variance 0.058 0.056

Do the data present sufficient evidence to indicate that the mean for population 1 is smaller than the mean for population 2? Use the p-value approach and the critical value approach and explain your conclusion.

Problem #2

A researcher believes she has designed a keyboard that is more efficient to use than a standard keyboard. In order to help decide if this is the case, typing speeds were taken for 8 different people on each keyboard. The lengths of time, in minutes, for each of the people to type a pre-selected manuscript are listed below. Assume the two population distributions are normal. Use the data to determine if the original keyboard yields slower times. Use a significance level of  = 0.05.

Person Original New
1 15 12
2 9 8
3 17 15
4 10 8
5 9 5
6 4 4
7 30 25
8 29 21

Problem #3

Assume that the population distributions of times (in minutes) for two different skiers to
race the same course are normal with equal variances. Two random samples, drawn
independently from the populations, showed the following statistics:

Construct and interpret a 95% confidence interval for the true difference in average time of skiers to race the same course.

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Independent random samples of 36 and 50 observations are drawn from two quantitative populations, 1 and 2, respectively. The sample data summary is shown here:

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