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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Question: The hot tamale caper. โHot tamalesโ are chewy, cinnamonflavored candies. A bulk vending machine is known to dispense, on average, 15 hot tamales per bag with a standard deviation of 3 per bag. Chance (Fall 2000) published an article on a classroom project in which students were required to purchase bags of hot tamales from the machine and count the number of candies per bag. One student group claimed they purchased five bags that had the following candy counts: 25, 23, 21, 21, and 20. These data are saved in the file. There was some question as to whether the students had fabricated the data. Use a hypothesis test to gain insight into whether or not the data collected by the students were fabricated. Use a level of significance that gives the benefit of the doubt to the students
Salaries of postgraduates. The Economics of Education Review (Vol. 21, 2002) published a paper on the relationship between education level and earnings. The data for the research was obtained from the National Adult Literacy Survey of more than 25,000 respondents. The survey revealed that males with a postgraduate degree have a mean salary of \(61,340 (with standard error \(Sx\) = \)2,185), while females with a postgraduate degree have a mean of \(32,227 (with standard error \(Sx\) = \)932).
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. \({H_0}:\mu = 10\), \({H_a}:\mu \ne 10\), \(\alpha = 0.05\), \(z = 1.96\)
Feminized faces in TV commercials. Television commercials most often employ females or โfeminizedโ males to pitch a companyโs product. Research published in Nature (August 27 1998) revealed that people are, in fact, more attracted to โfeminizedโ faces, regardless of gender. In one experiment, 50 human subjects viewed both a Japanese female face and a Caucasian male face on a computer. Using special computer graphics, each subject could morph the faces (by making them more feminine or more masculine) until they attained the โmost attractiveโ face. The level of feminization x (measured as a percentage) was measured.
a. For the Japanese female face, x = 10.2% and s = 31.3%. The researchers used this sample information to test the null hypothesis of a mean level of feminization equal to 0%. Verify that the test statistic is equal to 2.3.
b. Refer to part a. The researchers reported the p-value of the test as p = .021. Verify and interpret this result.
c. For the Caucasian male face, x = 15.0% and s = 25.1%. The researchers reported the test statistic (for the test of the null hypothesis stated in part a) as 4.23 with an associated p-value of approximately 0. Verify and interpret these results.
If you select a very small value for when conducting a hypothesis test, will tend to be big or small? Explain.
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