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Chapter 9: Q. 9.45 (page 364)

In each of Exercises 9.41-9.46 ,determine the critical values for a one-mean z-test. For each exercise, draw a graph that illustrates your answer

A right- tailed test with伪=0.01

Short Answer

Expert verified

A Right -tailed test with伪=0.01

In the right tail test that 伪=0.01, from normal local tables values are significant z0=2.33.

Step by step solution

01

Step 1. Given 

A right -tailed test with伪=0.01

02

Step 2. Graph 

A Right -tailed test with伪=0.01.

In the right tail test that 伪=0.01, from normal local tables values are significant z0=2.33.

The graph is shown below:

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Most popular questions from this chapter

As we mentioned on page 378, the following relationship holds between hypothesis test and confidence intervals for one-mean z-procedures: For a two-tailed hypothesis test at the significance level 伪, the null hypothesis role="math" localid="1653038937481" H0:渭=渭0will be rejected in favor of the alternative hypothesis Ha:渭鈮�渭0if and only if 渭0lies outside the 1-伪-level confidence interval for 渭. In each case, illustrate the preceding relationship by obtaining the appropriate one-mean z-interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

Part (a): Exercise 9.84

Part (b): Exercise9.87

Dementia is the loss of the in actual and social abilities severe enough to interfere with judging behavior and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onsite dementia: Exploring the Experience and Developing Evidence Guidelines for Practice", P Harris and J Keady explored the experiment struggles of people diagnosed with dementia and their familiar simple random sample \(21\) people with early-onset dementia the following data on age at diagnosis in years.

At the \(1%\) significance level, do the data provide sufficient evidence to conclude that the mean age at diagnosis of all people with early onset dementia is less than \(55\) years old? Assume that the population is standard deviation is \(6.8\) years.

As we mentioned on page \(378\), the following relationship holds between hypothesis tests and confidence intervals for one mean \(z-\)procedures: For a two-tailed hypothesis test at the significance level \(\alpha\), the null hypothesis \(H_{0}:\mu =\mu_{0}\) will be rejected in favor of the alternative hypothesis \(H_{a}:\mu \neq \mu_{0}\) if and only if \(\mu_{0}\) lies outside the \((1-\infty)\) level confidence interval for \(\mu\). In each case, illustrate the preceding relationship by obtaining the appropriate one-mean \(z-\)interval and comparing the result to the conclusion of the hypothesis test in the specified exercise.

a. Exercise \(9.84\)

b. Exercise \(9.87\)

Betting the Spreads. College basketball, and particularly the NCAA basketball tournament, is a popular venue for gambling, from novices in office betting pools to high rollers. To encourage uniforn betting across teams, Las Vegas oddsmakers assign a point spread to each game. The point spread is the oddsmakers" prediction for th number of points by which the favored team will win. If you bet of the favorite, you win the bet provided the favorite wins by more than the point spread; otherwise, you lose the bet. Is the point spread a good measure of the relative ability of the two teams? H. Stern and B. Mock addressed this question in the paper "College Basketball Upsets: Will a 16-Seed Ever Beat a 1-Seed?" (Chance, Vol. 11(1), pp. 27-31). They obtained the difference between the actual margin of victory and the point spread, called the point-spread error, for 2109 college basketball games. The mean point-spread error was found to be 鈭�0.2 point with a standard deviation of10.9 points. For a particular game, a point-spread error of 0 indicates that the point spread was a perfect estimate of the two teams' relative abilities.
(a) If, on average, the oddsmakers are estimating correctly, what is the (population) mean point-spread error?
(b) Use the data to decide, at the 5% significance level, whether the (population) mean point-spread error differs from 0 .
c) Interpret your answer in part (b).

We have been provided a sample mean, sample size, and population standard deviation. In the given case, use the one-mean z-test to perform the required hypothesis test at the 5% significance level.

x炉=23,n=15,蟽=4,H0:渭=22,Ha:渭>22
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