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Chapter 6: Q43 (page 241)
Critical Values. In Exercises 41–44, find the indicated critical value. Round results to two decimal places.
The indicated critical value of is 1.75.
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Sampling with Replacement The Orangetown Medical Research Center randomly selects 100 births in the United States each day, and the proportion of boys is recorded for each sample.
a. Do you think the births are randomly selected with replacement or without replacement?
b. Give two reasons why statistical methods tend to be based on the assumption that sampling is conducted with replacement, instead of without replacement.
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, theatre 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 females, find the first quartile , which is the length separating the bottom 25% from the top 75%.
Using a Formula to Describe a Sampling Distribution Exercise 15 “Births” requires the construction of a table that describes the sampling distribution of the proportions of girls from two births. Consider the formula shown here, and evaluate that formula using sample proportions (represented by x) of 0, 0.5, and 1. Based on the results, does the formula describe the sampling distribution? Why or why not?
Finding Bone Density Scores. In Exercises 37–40 assume that a randomly selected subject is given a bone density test. Bone density test scores are normally distributed with a mean of 0 and a standard deviation of 1. In each case, draw a graph, then find the bone density test score corresponding to the given information. Round results to two decimal places.
Find P10, the 10th percentile. This is the bone density score separating the bottom 10% from the top 90%.
Continuous Uniform Distribution. In Exercises 5–8, refer to the continuous uniform distribution depicted in Figure 6-2 and described in Example 1. Assume that a passenger is randomly selected, and find the probability that the waiting time is within the given range.
Less than 4.00 minutes
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