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Chapter 6: Q43 (page 241)

Critical Values. In Exercises 41鈥�44, find the indicated critical value. Round results to two decimal places.

z0.04

Short Answer

Expert verified

The indicated critical value of z0.04is 1.75.

Step by step solution

01

Given information

The critical value isz0.04

02

Describe the critical value 

The critical value is z伪for a particular value of 伪. Then, 伪is the area to the right of z伪.

Mathematically,

.PZ>z伪=伪

In this case, 伪=0.04, and PZ>z0.04=0.04.

03

Step 3: Simplify the term to obtain the cumulative probability

For obtaining the cumulative probability, simplify the term as follows.

Pz>z0.04=0.041-Pz<z0.04=0.04Pz<z0.04=0.96

From the standard normal table, the value of 0.96 is closest to 0.9599, and the corresponding row value of 1.7 and column value of 0.05 implies that the z value is 1.75.

04

Summarize the result

The value of z0.04=1.75has an area of 0.04 to its right. So, z0.04=1.75corresponds to a cumulative left area of 0.96.

Thus, the critical value is z0.04=1.75.

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Most popular questions from this chapter

In Exercises 13鈥�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

Find the probability that a female has a back-to-knee length greater than 24.0 in.

In Exercises 13鈥�20, use the data in the table below for sitting adult malesand females (based on anthropometric survey data from Gordon, Churchill, et al.). Thesedata 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

Significance Instead of using 0.05 for identifying significant values, use the criteria that a value x is significantly high if P(x or greater) 0.025 and a value is significantly low if P(x or less) 0.025. Find the female back-to-knee length, separating significant values from those that are not significant. Using these criteria, is a female back-to-knee length of 20 in. significantly low?

Small Sample Weights of golden retriever dogs are normally distributed. Samples of weights of golden retriever dogs, each of size n = 15, are randomly collected and the sample means are found. Is it correct to conclude that the sample means cannot be treated as being from a normal distribution because the sample size is too small? Explain.

Standard normal distribution, assume that a randomly selected subject is given a bone density test. Those 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 probability of the given bone density test score. If using technology instead of Table A-2, round answers to four decimal places.

Greater than -3.75

In Exercises 7鈥�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 Proportion

a. For the population, find the proportion of odd numbers.

b. Table 6-2 describes the sampling distribution of the sample mean. Construct a similar table representing the sampling distribution of the sample proportion of odd numbers. Then combine values of the sample proportion that 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 proportion of odd numbers.

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

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