Q7 Finding Critical Values. In Exer... [FREE SOLUTION] (2024)

Chapter 7: Q7 (page 311)

Finding Critical Values. In Exercises 5–8, find the critical value that corresponds to the given confidence level.

99.5%

Short Answer

Expert verified

The critical value $z_{\frac{α}{2}}$ for 99.5% level of confidence is 2.81.

Step by step solution

Given information

The level of significance is 99.5%.

Describe the concept of critical value

A critical value is a point on the test distribution that is compared to the test statistics to determine whether to reject the null hypothesis. It is denoted by $z_{\frac{α}{2}}$ which is equal to z score within the area of $\frac{α}{2}$ in the right tail of the standard normal distribution for $α$ level of significance.

Find the critical value

When finding a critical value $z_{\frac{α}{2}}$ for a particular value of $α$ , note thatis the cumulative area to the right of $z_{\frac{α}{2}}$ which implies that the cumulative area to the left of $z_{\frac{α}{2}}$ must be $1 - \frac{α}{2}$ .

Here, for 99.5% confidence level,

$α = 0.005 1 - \frac{α}{2} = 0.9975$

To find the z score corresponding the area 0.9975,

In the standard normal table for positive z score, find the value 0.9975, corresponding row value is 2.8, and column values is 0.01, which corresponds to the z-score of 2.81.

Therefore, the critical value for 99.5% level of significance is 2.81.

Most popular questions from this chapter

Sample Size. In Exercises 29–36, find the sample size required to estimate the population mean.Mean Weight of Male Statistics Students Data Set 1 “Body Data” in Appendix B includes weights of 153 randomly selected adult males, and those weights have a standard deviation of 17.65 kg. Because it is reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males, let σ=17.65 kg. How many male statistics students must be weighed in order to estimate the mean weight of all male statistics students? Assume that we want 90% confidence that the sample mean is within 1.5 kg of the population mean. Does it seem reasonable to assume that weights of male statistics students have less variation than weights of the population of adult males?In Exercises 5–8, use the relatively small number of given bootstrap samples to construct the confidence interval.Seating Choice In a 3M Privacy Filters poll, respondents were asked to identify their favourite seat when they fly, and the results include these responses: window, window, other, other. Letting “window” = 1 and letting “other” = 0, here are ten bootstrap samples for those responses: {0, 0, 0, 0}, {0, 1, 0, 0}, {0, 1, 0, 1}, {0, 0, 1, 0}, {1, 1, 1, 0}, {0, 1, 1, 0}, {1, 0, 0, 1}, {0, 1, 1, 1}, {1, 0, 1, 0}, {1, 0, 0, 1}. Using only the ten given bootstrap samples, construct an 80% confidence interval estimate of the proportion of respondents who indicated their favourite seat is “window.”Using Correct Distribution. In Exercises 5–8, assume that we want to construct a confidence interval. Do one of the following, as appropriate: (a) Find the critical valuetα2, (b) find the critical value zα2, or (c) state that neither the normal distribution nor the t distribution applies.Miami Heat Salaries Confidence level is 95%, σis not known, and the normal quantile plot of the 17 salaries (thousands of dollars) of Miami Heat basketball players is as shown.Determining Sample Size. In Exercises 19–22, assume that each sample is a simple random sample obtained from a normally distributed population. Use Table 7-2 on page 338 to find the indicated sample size.Space mountain You want to estimate σfor the population of waiting times for the space mountain ride in Walt Disney World. You want to be 99% confident that the sample standard deviation is within 1% ofσ. Find the minimum sample size. Is this sample size practical?Sample Size. In Exercises 29–36, find the sample size required to estimate the population mean.Mean Pulse Rate of Males Data Set 1 “Body Data” in Appendix B includes pulse rates of 153 randomly selected adult males, and those pulse rates vary from a low of 40 bpm to a high of 104 bpm. Find the minimum sample size required to estimate the mean pulse rate of adult males. Assume that we want 99% confidence that the sample mean is within 2 bpm of the population mean.a. Find the sample size using the range rule of thumb to estimate σ.b. Assume that σ=11.3 bpm, based on the value of s=12.5 bpmfor the sample of 153 male pulse rates.c. Compare the results from parts (a) and (b). Which result is likely to be better?

See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Mechanics Maths

Read Explanation

Decision Maths

Read Explanation

Discrete Mathematics

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

This website uses cookies to improve your experience. We'll assume you're ok with this, but you can opt-out if you wish. Accept