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Chapter 8: Q3BSC (page 356)

t Test Exercise 2 refers to a t test. What is the t test? Why is the letter t used? What is unrealistic about the z test methods in Part 2 of this section?

Short Answer

Expert verified

T-test is a statistical method to find the significant difference between the means. The letter t is used because the result is based on the t-values.

Since the population standard deviation is unknown, z-test cannot be used.

Step by step solution

01

Given information

Refer to Exercise 2 for the t-test on duration times of alcohol use for 12 different video games.

02

Describe t-test

T-test is a method to check the claims concerning the population mean values. The letter t is used because the test result is based on t-distribution values (test statistic follows student’s t-distribution).

03

Explain the use of z-test

Z-test is applied when the population is known to be normal, and the selection method is known to be random along with aknown measure of population standard deviation.

It is a method used to test the claims concerning the population mean values, where the actual value of the mean is unidentified. The unrealistic part of the z-test method is that it is highly unusual to obtain the exact value of population standard deviation for such populations where the true mean is unidentified.

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Most popular questions from this chapter

In Exercises 1–4, use these results from a USA Today survey in which 510 people chose to respond to this question that was posted on the USA Today website: “Should Americans replace passwords with biometric security (fingerprints, etc)?” Among the respondents, 53% said “yes.” We want to test the claim that more than half of the population believes that passwords should be replaced with biometric security.

Null and Alternative Hypotheses Identify the null hypothesis and alternative hypothesis.

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?

Test Statistics. In Exercises 13–16, refer to the exercise identified and find the value of the test statistic. (Refer to Table 8-2 on page 362 to select the correct expression for evaluating the test statistic.)

Exercise 5 “Online Data”

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 “there is sufficient evidence to support the claim that the mean height of men is equal to 174.1 cm”?

Finding Critical t Values When finding critical values, we often need significance levels other than those available in Table A-3. Some computer programs approximate critical t values by calculating t=df×eA2/df-1where df = n-1, e = 2.718, A=z8×df+3/8×df+1, and z is the critical z score. Use this approximation to find the critical t score for Exercise 12 “Tornadoes,” using a significance level of 0.05. Compare the results to the critical t score of 1.648 found from technology. Does this approximation appear to work reasonably well?
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