Homework SourseAccording to an article by George Will San Jose Mercury News
According to an article by George Will (San Jose Mercury News, Feb. 28, 2002), the average U.S. consumption per person per year of french fries is 28 pounds. You think that the average in Prince George’s County might be different. You randomly survey 50 people in this county. The sample average is 25.8 pounds with a sample standard deviation of 10.3 pounds. a.
a. Conduct an appropriate hypothesis test at the 0.05 level of significance to determine whether the average is different from 28 pounds in PG County. You may use your calculator, but for complete credit, make sure you state 1) the hypotheses, 2) the appropriate test statistic (z or t) and its value, 3) the p-value, 4) your statistical conclusion, and 5) your practical conclusion. Organize your answers clearly to receive full credit.
b. Would you expect a 95% confidence interval to contain the value of 28 pounds? Explain why or why not based on your answer to part a.
Solution
a)
1)
Formulating the null and alternative hypotheses,
Ho: u = 28
Ha: u =/ 28 [ANSWERS]
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2)
As we can see, this is a two tailed test.
Here, we use z, as n > 30.
Getting the test statistic, as
X = sample mean = 25.8
uo = hypothesized mean = 28
n = sample size = 50
s = standard deviation = 10.3
Thus, z = (X - uo) * sqrt(n) / s = -1.510325164 [ANSWER, TEST STATISTIC]
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3)
Thus, the p value is, as it is two tailed,
p = 0.130960474 [ANSWER]
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4)
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS. [ANSWER]
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5)
Thus, there is no significant evidence that the average consumption per person per year of french fries in Prince George’s County is different from the US average.
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b)
YES, because the P value is greater than 0.05 (1-0.95).
