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Chapter 8: Q. 9.18 (page 358)

Early-Onset Dementia. Dementia is the loss of the intellectual and social abilities severe enough to interfere with judgment, behavior, and daily functioning. Alzheimer's disease is the most common type of dementia. In the article "Living with Early Onset Dementia: Exploring the Experience and Developing Evidence Based Guidelines for Practice" (Alzheimer's Care Quarterly, Vol. 5, Issue 2, pp. 111-122), P. Harris and J. Keady explored the experience and struggles of people diagnosed with dementia and their families. A hypothesis test is to be performed to decide whether the mean age at diagnosis of all people with early-onset dementia is less than 55 years old.

Short Answer

Expert verified

Part (a). 55 years

Part (b). less than 55 years

Part (c). left-tailed test

Step by step solution

01

Part (a) Step 1. Given information.  

To determine whether the average age upon diagnosis of all persons with early-onset dementia is less than 55 years old, a hypothesis test will be conducted.

02

Part (a) Step 2. Determine the null hypothesis.  

Let

渭=the mean age at diagnosis of all people with early-onset dementia. The mean age at diagnosis of all people with early-onset dementia u is equal to 55 years.

The null hypothesis:

So,H0:=55years

03

Part (b) Step 1. Determine the alternative hypothesis.  

The alternative idea is that all patients with early-onset dementia u are diagnosed while they are under 55 years old.

So,H0:H<55years

04

Part (c) Step 1. Classify the hypothesis test as two tailed, left tailed, or right tailed.  

This hypothesis test is a left tailed test. This is because the mean age at diagnosis of all people with early-onset dementia 渭is less than 55 is decided by performing the alternative hypothesis test.

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Most popular questions from this chapter

A formal hypothesis test is to be conducted using the claim that the mean height of men is equal to 174.1 cm.

a. What is the null hypothesis, and how is it denoted?

b. What is the alternative hypothesis, and how is it denoted?

c. What are the possible conclusions that can be made about the null hypothesis?

d. Is it possible to conclude that 鈥渢here is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm鈥�?

Confidence interval Assume that we will use the sample data from Exercise 1 鈥淰ideo Games鈥� with a 0.05 significance level in a test of the claim that the population mean is greater than 90 sec. If we want to construct a confidence interval to be used for testing the claim, what confidence level should be used for the confidence interval? If the confidence interval is found to be 21.1 sec < 渭< 191.4 sec, what should we conclude about the claim?

Using Confidence Intervals to Test Hypotheseswhen analyzing the last digits of telephone numbers in Port Jefferson, it is found that among 1000 randomly selected digits, 119 are zeros. If the digits are randomly selected, the proportion of zeros should be 0.1.

a.Use the critical value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

b.Use the P-value method with a 0.05 significance level to test the claim that the proportion of zeros equals 0.1.

c.Use the sample data to construct a 95% confidence interval estimate of the proportion of zeros. What does the confidence interval suggest about the claim that the proportion of zeros equals 0.1?

d.Compare the results from the critical value method, the P-value method, and the confidence interval method. Do they all lead to the same conclusion?

Finding P-values. In Exercises 5鈥�8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value7. Old Faithful. The claim is that for the duration times (sec) of eruptions of the Old Faithful geyser, the mean is 渭=240sec. The sample size is n = 6 and the test statistic is t = 1.340.

Final Conclusions. In Exercises 25鈥�28, use a significance level of = 0.05 and use the given information for the following:

a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)

b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.

Original claim: Fewer than 90% of adults have a cell phone. The hypothesis test results in a P-value of 0.0003.
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