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Chapter 9: Q7CRE (page 414)

Braking Reaction Times: Normal? The accompanying normal quantile plot is obtained by using the braking reaction times of females listed in Exercise 6. Interpret this graph.

Short Answer

Expert verified

The normal quartile plot indicates that the data of braking reaction time of females is taken from the normal population.

Step by step solution

01

Given information

The normality plot for braking reaction times of females is given.

02

Describe the normal probability plot

A normal quartile plot maps observations against the z-scores to establish the normality among dataset.

Two conditions may follow:

  • If the observations are aligned in a straight line, they are taken from a normally distributed population.
  • If the observations are not aligned in a straight line, theyare taken from a non-normal population.
03

Interpret the normality plot

The green line depicts an approximate trend of the observations marked with blue dots.

All the observations either fall on the line or are very close to the line. Thus, the plot indicates that the underlying population of braking reaction timeforall females is normally distributed.

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Most popular questions from this chapter

Testing Claims About Proportions. In Exercises 7โ€“22, test the given claim. Identify the null hypothesis, alternative hypothesis, test statistic, P-value or critical value(s), then state the conclusion about the null hypothesis, as well as the final conclusion that addresses the original claim.

License Plate Laws The Chapter Problem involved passenger cars in Connecticut and passenger cars in New York, but here we consider passenger cars and commercial trucks. Among2049 Connecticut passenger cars, 239 had only rear license plates. Among 334 Connecticuttrucks, 45 had only rear license plates (based on samples collected by the author). A reasonable hypothesis is that passenger car owners violate license plate laws at a higher rate than owners of commercial trucks. Use a 0.05 significance level to test that hypothesis.

a. Test the claim using a hypothesis test.

b. Test the claim by constructing an appropriate confidence interval.

In Exercises 5โ€“20, assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. (Note: Answers in Appendix D include technology answers based on Formula 9-1 along with โ€œTableโ€ answers based on Table A-3 with df equal to the smaller of n1โˆ’1 and n2โˆ’1.)

Coke and Pepsi Data Set 26 โ€œCola Weights and Volumesโ€ in Appendix B includes volumes of the contents of cans of regular Coke (n = 36, x = 12.19 oz, s = 0.11 oz) and volumes of the contents of cans of regular Pepsi (n = 36, x = 12.29 oz, s = 0.09 oz).

a. Use a 0.05 significance level to test the claim that cans of regular Coke and regular Pepsi have the same mean volume.

b. Construct the confidence interval appropriate for the hypothesis test in part (a).

c. What do you conclude? Does there appear to be a difference? Is there practical significance?

Determining Sample Size The sample size needed to estimate the difference between two population proportions to within a margin of error E with a confidence level of 1 - a can be found by using the following expression:

E=zฮฑ2p1q1n1+p2q2n2

Replace n1andn2 by n in the preceding formula (assuming that both samples have the same size) and replace each of role="math" localid="1649424190272" p1,q1,p2andq2by 0.5 (because their values are not known). Solving for n results in this expression:

n=zฮฑ222E2

Use this expression to find the size of each sample if you want to estimate the difference between the proportions of men and women who own smartphones. Assume that you want 95% confidence that your error is no more than 0.03.

Confidence Interval for Haemoglobin

Large samples of women and men are obtained, and the haemoglobin level is measured in each subject. Here is the 95% confidence interval for the difference between the two population means, where the measures from women correspond to population 1 and the measures from men correspond to population 2:\(\)\( - 1.76g/dL < {\mu _1} - {\mu _2} < - 1.62g/dL\).

a. What does the confidence interval suggest about equality of the mean hemoglobin level in women and the mean hemoglobin level in men?

b. Write a brief statement that interprets that confidence interval.

c. Express the confidence interval with measures from men being population 1 and measures from women being population 2.

Using Confidence Intervals

a. Assume that we want to use a 0.05 significance level to test the claim that p1 < p2. Which is better: A hypothesis test or a confidence interval?

b. In general, when dealing with inferences for two population proportions, which two of the following are equivalent: confidence interval method; P-value method; critical value method?

c. If we want to use a 0.05 significance level to test the claim that p1 < p2, what confidence level should we use?

d. If we test the claim in part (c) using the sample data in Exercise 1, we get this confidence interval: -0.000508 < p1 - p2 < - 0.000309. What does this confidence interval suggest about the claim?
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