Name(s)                                                                              :
Math 203 A, Introduction to Statistics Quiz 3
Tom Linton, Fall 2000, Central College
  1. Assume that the yield per acre for a new variety of corn follows a normal distribution with unknown mean m and standard deviation s = 10 bushels per acre. An agricultural researcher plants twenty-five plots of land (one acre each) with the new variety of corn. The average yield for these twenty-five plots is  = 150 bushels per acre.
    1. Give a 90% confidence interval for m, the mean yield per acre for this variety of corn.

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    2. In everyday language (or some close approximation to everyday language), explain what the interval from part (a) tells you about the mean yield per acre.

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    3. If we calculated a 99% confidence interval for m instead of a 90% confidence interval, would the new interval (the 99% confidence interval) be wider or narrower than the old one?

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    4. If I wanted the margin of error for the 99% confidence interval to be 0.5 bushels, how large would n have to be?

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  2. Assume that with careful eating, the average person can lose 10 pounds in five weeks, and that the standard deviation of individuals' weight loss is s = 2 pounds (in five weeks). In their advertisements, a new diet program would like to claim that their methods result in a mean weight loss of more than ten pounds in five weeks. In order to determine if this is a valid claim, they hire an independent testing agency that then selects twenty-five random people to be placed on this diet. The agency calculates  = the average weight loss (in five weeks) of the 25 individuals.
    1. What are the null and alternative hypothesis?

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    2. What is the approximate distribution of the statistic ? Draw a density curve for the distribution of  values.

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    3. Suppose that the agency obtained the value = 10.83 pounds (in five weeks) for the twenty-five persons in the random sample. Mark this value on your plot from part (c), shade in the area that corresponds to the p-value of this test, and calculate the p-value.

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    4. In plain English, what does your p-value tell you and what sort of evidence does it provide?

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    5. Is the result above (=10.83 pounds) significant at the 5% level?