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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鈥檚 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

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脳eA2/df-1where df = n-1, e = 2.718, A=z8脳df+3/8脳df+1, and z is the critical z score. Use this approximation to find the critical t score for Exercise 12 鈥淭ornadoes,鈥� 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?

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 Technology. In Exercises 5鈥�8, identify the indicated values or interpret the given display. Use the normal distribution as an approximation to the binomial distribution, as described in Part 1 of this section. Use = 0.05 significance level and answer the following:

a. Is the test two-tailed, left-tailed, or right-tailed?

b. What is the test statistic?

c. What is the P-value?

d. What is the null hypothesis, and what do you conclude about it?

e. What is the final conclusion?

Biometric Security In a USA Today survey of 510 people, 53% said that we should replace passwords with biometric security, such as fingerprints. The accompanying Statdisk display results from a test of the claim that half of us say that we should replace passwords with biometric security.

Interpreting Power For the sample data in Example 1 鈥淎dult Sleep鈥� from this section, Minitab and StatCrunch show that the hypothesis test has power of 0.4943 of supporting the claim that 渭<7 hours of sleep when the actual population mean is 6.0 hours of sleep. Interpret this value of the power, then identify the value of 尾and interpret that value. (For the t test in this section, a 鈥渘oncentrality parameter鈥� makes calculations of power much more complicated than the process described in Section 8-1, so software is recommended for power calculations.)

Hypothesis Test with Known 蟽 How do the results from Exercise 13 鈥淐ourse Evaluations鈥� change if 蟽is known to be 0.53? Does the knowledge of 蟽 have much of an effect?
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