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Chapter 10: Q. T10.4 (page 698)

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t Interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom's confidence interval is wider.

(b) Janelle's confidence Interval is wider.

(c) Both confidence Intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake, degrees of freedom has to be a whole number.

Short Answer

Expert verified

The correct answer is:

(a) Tom's confidence interval is wider.

Step by step solution

01

Given information

We are given that Janelle uses a higher degree of freedom than Tom.

02

Explanation

A higher degree of freedom results in a lowert*-value.

A lower t*-valueresults in a lower margin of error and thus also a narrower confidence interval.

Then we know that Janelle's confidence interval is narrower than Tom's confidence interval, or Tom's confidence interval is wider than Janelle's confidence level.

Thus answer (a) is correct.

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Most popular questions from this chapter

Thirty-five people from a random sample of 125 workers from Company A admitted

to using sick leave when they weren’t really ill. Seventeen employees from a random

sample of 68 workers from Company B admitted that they had used sick leave when

they weren’t ill. Which of the following is a 95% confidence interval for the difference

in the proportions of workers at the two companies who would admit to using sick

leave when they weren’t ill?

(a) 0.03±(0.28)(0.72)125+(0.25)(0.75)68

(b) 0.03±1.96(0.28)(0.72)125+(0.25)(0.75)68

(c) 0.03±1.645(0.28)(0.72)125+(0.25)(0.75)68

(d) 0.03±1.96(0.269)(0.731)125+(0.269)(0.731)68

(e)0.03±1.645(0.269)(0.731)125+(0.269)(0.731)68

TicksLyme disease is spread in the northeastern United States by infected ticks. The ticks are infected mainly by feeding on mice, so more mice result in more infected ticks. The mouse population, in turn, rises and falls with the abundance of acorns, their favored food. Experimenters studied two similar forest areas in a year when the acorn crop failed. To see if mice are more likely to breed when there are more acorns, the researchers added hundreds of thousands of acorns to one area to imitate an abundant acorn crop, while leaving the other area untouched. The next spring, 54of the 72mice trapped in the first area were in breeding condition, versus 10of the 17mice trapped in the second area.

a. State appropriate hypotheses for performing a significance test. Be sure to define the parameters of interest.

b. Check if the conditions for performing the test are met.

Better barley Does drying barley seeds in a kiln increase the yield of barley? A famous experiment by William S. Gosset (who discovered the t distributions) investigated this question. Eleven pairs of adjacent plots were marked out in a large field. For each pair, regular barley seeds were planted in one plot and kiln-dried seeds were planted in the other. A coin flip was used to determine which plot in each pair got the regular barley seed and which got the kiln-dried seed. The following table displays the data on barley yield (pound per acre) for each plot.

Do these data provide convincing evidence at the α=0.05level that drying barley seeds in a kiln increases the yield of barley, on average?

Suppose the true proportion of people who use public transportation to get to work in the Washington, D.C. area is 0.45. In a simple random sample of 250people who work in Washington, about how far do you expect the sample proportion to be from the true proportion?

a. 0.4975

b. 0.2475

c. 0.0315

d. 0.0009

e.0

A study of road rage asked separate random samples of 596men and 523 women

about their behavior while driving. Based on their answers, each respondent was

assigned a road rage score on a scale of 0 to 20. Are the conditions for performing a

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a. Maybe; we have independent random samples, but we should look at the data to

check Normality.

b. No; road rage scores on a scale from 0 to 20 can’t be Normal.

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d. Yes; the large sample sizes guarantee that the corresponding population

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e. Yes; we have two independent random samples and large sample sizes.
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