Chapter 7: Q116S (page 442)
A t-test is conducted for the null hypothesis versus the alternative for a random sample of n = 17 observations. The test results are t = 1.174, p-value = 0.1288.
a. Interpret the p-value.
a. There is a 12.88% chance that we would observe a test statistic resulting in 1.174.
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For each of the following situations, determine the p-value and make the appropriate conclusion.
a.\({H_0}:\mu \le 25\),\({H_a}:\mu > 25\),\(\alpha = 0.01\),\(z = 2.02\)
b.\({H_0}:\mu \ge 6\),\({H_a}:\mu < 6\),\(\alpha = 0.05\),\(z = - 1.78\)
c.\({H_0}:\mu = 110\),\({H_a}:\mu \ne 110\),\(\alpha = 0.1\),\(z = - 1.93\)
d. \({H_0}:\mu = 10\), \({H_a}:\mu \ne 10\), \(\alpha = 0.05\), \(z = 1.96\)
Question: Point spreads of NFL games. Refer to the Chance (Fall 1998) study of point-spread errors in NFL games, Exercise 7.41 (p. 411). Recall that the difference between the actual game outcome and the point spread established by odds makers—the point-spread error—was calculated for 240 NFL games. The results are summarized as follows: . Suppose the researcher wants to know whether the true standard deviation of the point spread errors exceeds 15. Conduct the analysis using α = 0.10.
Complete the following statement: The smaller the p-value associated with a test of hypothesis, the stronger the support for the _____ hypothesis. Explain your answer.
In a test of the hypothesis versus, a sample of n = 100 observations possessed meanand standard deviation s = 4.1. Find and interpret the p-value for this test.
EPA limits on vinyl chloride. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey Department of Health, Hazardous Substance Fact Sheet, 2010). A major plastics manufacturer, attempting to control the amount of vinyl chloride its workers are exposed to, has given instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm. A random sample of 50 air specimens produced the following statistics: \(\overline x = 3.1\)ppm,\(s = 0.5\)ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use\(\alpha = 0.01\).
b. If you were the plant manager, would you want to use a large or a small value for\(\alpha \)the test in part a? Explain.
c. Find the p-value for the test and interpret its value
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