Chapter 7: Q109S (page 441)
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.
Short Answer
Alternative hypothesis.
Chapter 7: Q109S (page 441)
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.
Alternative hypothesis.
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Get started for freeRadon exposure in Egyptian tombs. Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in Egyptian tombs, Exercise 6.30 (p. 349). The radon levels—measured in becquerels per cubic meter (\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) )—in the inner chambers of a sample of 12 tombs are listed in the table shown below. For the safety of the guards and visitors, the Egypt Tourism Authority (ETA) will temporarily close the tombs if the true mean level of radon exposure in the tombs rises to 6,000\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) . Consequently, the ETA wants to conduct a test to determine if the true mean level of radon exposure in the tombs is less than 6,000\({{Bq} \mathord{\left/ {\vphantom {{Bq} {{m^3}}}} \right. \\} {{m^3}}}\) , using a Type I error probability of .10. An SPSS analysis of the data is shown at the bottom of the page. Specify all the elements of the test: \({H_0}\,,{H_a}\) test statistic, p-value,\(\alpha \) , and your conclusion.
50 910 180 580 7800 4000 390 12100 3400 1300 11900 110
Ages of cable TV shoppers. Cable TV’s Home Shopping Network (HSN) reports that the average age of its shoppers is 52 years. Suppose you want to test the null hypothesis,\({H_0}:\mu = 52\), using a sample of\(n = 50\) cable TV shoppers.
a. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)
b. Find the p-value of an upper-tailed test if\(\overline x = 53.3\)and\(s = 7.1\)
c. Find the p-value of a two-tailed test if\(\overline x = 53.3\)and\(s = 10.4\)
d. For each of the tests, parts a–c, give a value of\(\alpha \)that will lead to a rejection of the null hypothesis.
e. If\(\overline x = 53.3\), give a value of s that will yield a two-tailed p-value of 0.01 or less.
Consider the test \({H_0}:\mu = 70\) versus \({H_a}:\mu \ne 70\) using a large sample of size n = 400. Assume\(\sigma = 20\).
a. Describe the sampling distribution of\(\bar x\).
b. Find the value of the test statistic if\(\bar x = 72.5\).
c. Refer to part b. Find the p-value of the test.
d. Find the rejection region of the test for\(\alpha = 0.01\).
e. Refer to parts c and d. Use the p-value approach to
make the appropriate conclusion.
f. Repeat part e, but use the rejection region approach.
g. Do the conclusions, parts e and f, agree?
Suppose you are interested in conducting the statistical test of \({H_0}:\mu = 255\) against \({H_a}:\mu > 225\), and you have decided to use the following decision rule: Reject H0 if the sample mean of a random sample of 81 items is more than 270. Assume that the standard deviation of the population is 63.
a. Express the decision rule in terms of z.
b. Find \(\alpha \), the probability of making a Type I error by using this decision rule.
Cooling method for gas turbines. During periods of high electricity demand, especially during the hot summer months, the power output from a gas turbine engine can drop dramatically. One way to counter this drop in power is by cooling the inlet air to the gas turbine. An increasingly popular cooling method uses high-pressure inlet fogging. The performance of a sample of 67 gas turbines augmented with high-pressure inlet fogging was investigated in the Journal of Engineering for Gas Turbines and Power (January 2005). One performance measure is heat rate (kilojoules per kilowatt per hour). Heat rates for the 67 gas turbines are listed in the table below. Suppose that standard gas turbines have heat rates with a standard deviation of 1,500 kJ/kWh. Is there sufficient evidence to indicate that the heat rates of the augmented gas turbine engine are more variable than the heat rates of the standard gas turbine engine? Test using a = .05.
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