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Chapter 8: Q. R8.5 (page 548)

Engine parts A random sample of 16 of the more than 200auto engine crankshafts produced in one day was selected. Here are measurements (in millimeters) of a critical component on these crankshafts:

a. Construct and interpret a 95%confidence interval for the mean length of this component on all the crankshafts produced on that day.

b. The mean length is supposed to be 渭=224mm but can drift away from this target during production. Does your interval from part (a) suggest that the mean has drifted from 224mm? Explain your answer.

Short Answer

Expert verified

Part a) The confidence interval is (223.971,224.0.33)

Part b) No, it has not drifted from24mm

Step by step solution

01

Part a) Step 1: Given information

The data set is

02

Part a) Step 2: The objective is to find out the 95%confidence interval for the mean length of the component.

We know,

The formula to compute the t- confidence interval for the population mean is:

CI=x炉卤t伪/2,df脳sn

Because the population standard deviation is unknown, the t-confidence interval should be used.

The obtained excel output is:

Therefore, the required confidence interval is(223.971,224.033)

03

Part b) Step 1: The objective is to explain whether the mean has drifted from 224 mm 

The confidence interval is known from the preceding(223.971,224.033) Since the upper limit is224.033, which is greater than224. As a result, the mean cannot be said to have deviated from 224mm

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Most popular questions from this chapter

Shoes The AP Statistics class in Exercise 1 also asked an SRS of 20boys at their school how many pairs of shoes they have. A 95%confidence interval for 渭G-渭B=the true difference in the mean number of pairs of shoes for girls and

boys is 10.9to26.5.

a. Interpret the confidence interval.

b. Does the confidence interval give convincing evidence of a difference in the true mean number of pairs of shoes for boys and girls at the school? Explain your answer.

Gambling and the NCAA Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594Division Imale athletes who responded to the survey, 3547reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1%margin of error.

a. The confidence level was not stated in the report. Use what you have learned to

estimate the confidence level, assuming that the NCAA took an SRS.

b. The study was designed to protect the anonymity of the student athletes who responded. As a result, it was not possible to calculate the number of students who were asked to respond but did not. How does this fact affect the way that you interpret the results?

Critical values What critical value t*from Table B should be used for a

confidence interval for the population mean in each of the following situations?

a. A 95% confidence interval based on n=10 randomly selected observations

b. A99% confidence interval from an SRS of 20 observations

c. A 90% confidence interval based on a random sample of 77 individuals

Check whether each of the conditions is met for calculating a confidence interval for the population proportion

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a. How large a sample must you test to estimate the proportion of PTC tasters within 0.04with 90%confidence? Answer this question using the 75%estimate as the guessed value for p^.

b. Answer the question in part (a) again, but this time use the conservative guessp^=0.5. By how much do the two sample sizes differ?
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