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Chapter 7: Q13E (page 398)

Calories in school lunches. A University of Florida economist conducted a study of Virginia elementary school lunch menus. During the state-mandated testing period, school lunches averaged 863 calories (National Bureau of Economic Research, November 2002). The economist claims that after the testing period ends, the average caloric content of Virginia school lunches drops significantly. Set up the null and alternative hypotheses to test the economist鈥檚 claim.

Short Answer

Expert verified

The null and the alternative hypotheses are H0: 渭0 = 863 and Ha: 渭a< 863.

Step by step solution

01

Given information

As per National Bureau of Economic Research, the schools launch averaged 863 calories during the state-mandated testing period.

02

Setting up the hypotheses

The null hypothesis is the assumed-true hypothesis, while the alternative is the hypothesis that must demonstrate with the data. Because the researcher is attempting to prove that the lunch calories drop from 863 calories, data must be used to confirm this hypothesis. The null hypothesis is thus that the caloric value of lunches doesn鈥檛 fall below 863 calories after the testing, while the alternative hypothesis is that the caloric value of school lunches does drop below 863 calories after the end of the test period. That is,

H0: 渭0 = 863

Ha: 渭a < 863

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Most popular questions from this chapter

A simple random sample of 25 observations was selected from a normal population. The mean and standard deviation of this sample are 20 and 5, respectively.

a. Test H0:渭=22against Ha:渭鈮�22at the 10% significance level.

b. Test H0:渭鈮�22against H0:渭鈮�22at the 1% significance level.

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The data (where higher point values indicate a higher level of support for sustainability) are saved in the accompanying file. The CEO of a

CPA firm claims that the true mean level of support for sustainability is 75 points.

a. Specify the null and alternative hypotheses for testing this claim.

b. For this problem, what is a Type I error? A Type II error?

c. The XLSTAT printout shown above gives the results of the test. Locate the test statistic and p-value on the printout.

d. At 伪 = .05, give the appropriate conclusion.

e. What assumptions, if any, about the distribution of support levels must hold true in order for the inference derived from the test to be valid? Explain.

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鈥淢ade in the USA鈥� survey. Refer to the Journal of Global Business (Spring 2002) study of what 鈥淢ade in the USA鈥� means to consumers, Exercise 2.154 (p. 143). Recall that 64 of 106 randomly selected shoppers believed 鈥淢ade in the USA鈥� means 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe 鈥淢ade in the USA鈥� means 100% of labor and materials are from the United States.

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We reject the null hypothesis when the test statistic falls in the rejection region, but we do not accept the null hypothesis when the test statistic does not fall in the rejection region. Why?

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