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Chapter 8: Q3 (page 396)

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 a known 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 9–12, refer to the exercise identified. Make subjective estimates to decide whether results are significantly low or significantly high, then state a conclusion about the original claim. For example, if the claim is that a coin favours heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favours heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).

Exercise 7 “Pulse Rates”

Testing Hypotheses. In Exercises 13–24, assume that a simple random sample has been selected and test the given claim. Unless specified by your instructor, use either the P-value method or the critical value method for testing hypotheses. Identify the null and alternative hypotheses, test statistic, P-value (or range of P-values), or critical value(s), and state the final conclusion that addresses the original claim.

How Many English Words? A simple random sample of 10 pages from Merriam-Webster’s Collegiate Dictionary is obtained. The numbers of words defined on those pages are found, with these results: n = 10, x = 53.3 words, s = 15.7 words. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.0 words. Assume a normally distributed population. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.0 words. What does the result suggest about the claim that there are more than 70,000 defined words?

Estimates and Hypothesis Tests Data Set 3 “Body Temperatures” in Appendix B includes sample body temperatures. We could use methods of Chapter 7 for making an estimate, or we could use those values to test the common belief that the mean body temperature is 98.6°F. What is the difference between estimating and hypothesis testing?

P-Values. In Exercises 17–20, do the following:

a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.

b. Find the P-value. (See Figure 8-3 on page 364.)

c. Using a significance level of = 0.05, should we reject H0or should we fail to reject H0?

The test statistic of z = -1.94 is obtained when testing the claim that p=38 .

Finding P-values. In Exercises 5–8, either use technology to find the P-value or use Table A-3 to find a range of values for the P-value.

Airport Data Speeds: The claim that for Verizon data speeds at airports, the mean. The sample size is and the test statistic is

t =-1.625 .
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