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Chapter 6: Q6 (page 281)

Interpreting Normal Quantile Plots.In Exercises 5–8, examine the normal quantile plot and determine whether the sample data appear to be from a population with a normal distribution.

Diet Pepsi The normal quantile plot represents weights (pounds) of the contents of cans of Diet Pepsi from Data Set 26 “Cola Weights and Volumes” in Appendix B.

Short Answer

Expert verified

From the given normal quantile plot, it appears that the sample data of weights(pounds) of the contents of cans of Diet Pepsi is from a population that follows the normal distribution because the points on the plot follow a straight line pattern.

Step by step solution

01

Given information

The normal quantile plot of the sample data of weights (pounds) of the contents of cans of Diet Pepsi is constructed.

02

Step 2:Interpretation of the normal quantile plot

In a normal quantile plot, if the points form a straight-line pattern, then the sample is said to be taken from a normally distributed population.

Here, the points on the plot lie close to the straight line.

Therefore, the sample ofweights (pounds) of the contents of cans of Diet Pepsi appears to be from a normally distributed population.

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Most popular questions from this chapter

In Exercises 13–20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Mean

St.Dev.

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

For males, find P90, which is the length separating the bottom 90% from the top 10%.

In Exercises 13–20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Sitting Back-to-Knee Length (Inches)

Mean

St. Dev

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) ≤ 0.01 and a value is significantly low if P(x or less) ≤ 0.01. Find the back-to-knee lengths for males, separating significant values from those that are not significant. Using these criteria, is a male back-to-knee length of 26 in. significantly high?

:In Exercises 13–20, use the data in the table below for sitting adult males and females (based on anthropometric survey data from Gordon, Churchill, et al.). These data are used often in the design of different seats, including aircraft seats, train seats, the theater seats, and classroom seats. (Hint: Draw a graph in each case.)

Mean

St.Dev.

Distribution

Males

23.5 in

1.1 in

Normal

Females

22.7 in

1.0 in

Normal

Find the probability that a male has a back-to-knee length less than 21 in.

In Exercises 9–12, find the indicated IQ score and round to the nearest whole number. The graphs depict IQ scores of adults, and those scores are normally distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler IQ test).

In Exercises 7–10, use the same population of {4, 5, 9} that was used in Examples 2 and 5. As in Examples 2 and 5, assume that samples of size n = 2 are randomly selected with replacement.

Sampling Distribution of the Sample Variance

a. Find the value of the population variance σ2.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample variance s2. Then combine values of s2that are the same, as in Table 6-3 (Hint: See Example 2 on page 258 for Tables 6-2 and 6-3, which describe the sampling distribution of the sample mean.)

c. Find the mean of the sampling distribution of the sample variance.

d. Based on the preceding results, is the sample variance an unbiased estimator of the population variance? Why or why not?
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