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18. The average loan debt for college seniors is $20,262. If the debt is normally distributed...

18. The average loan debt for college seniors is $20,262. If the debt is normally distributed with a standard deviation of $5100, find these probabilities: (3 points each)

  1. Find the probability that a randomly selected senior owes at least $21,000.  

    1. Find the probability that the mean debt from a sample of 20 seniors falls between $20,000 and $21,000.
  2. (3 points) The average weight of a package of rolled oats is supposed to be at least 18 ounces. A sample of 18 packages shows a mean of 17.78 ounces with a standard deviation of 0.41 ounces. The calculated test statistic is t = -2.28 (left tail test) and the corresponding p-value = 0.018.

  3. Based on the results above, is the sample mean (17.78 ounces) smaller than the specification (18 ounces) at the 0.05 level of significance? (Check one of the following responses):

    A. Yes, the sample mean is significantly smaller than the specification at 0.05 level of significance.

    B. No, the sample mean is not significantly smaller than the specification at 0.05 level of significance.

    C. Yes, the p-value is greater than the alpha level.

    D. No, the p-value is lower than 0.01

    ACME Manufacturing claims that its cell phone batteries last more than 32 hours on average in a certain type of cell phone. Tests on a random sample of 18 batteries showed a mean battery life of 37.8 hours with a population standard deviation of 10 hours. Is the mean battery life greater than the 32 hour claim? Answer the following questions using a significance level of alpha = 0.05.

    Test statistic formula:

    25. (2 points) Write the null and alternative hypotheses:

    H0:

    H1:

    26. (2 points) In the box above, show the formula for calculating the appropriate test statistic. Include actual numbers in the formula, for example, z or t = (32-32)/32.

    27. (2 points) Calculate the appropriate test statistic:   _____________

    29. (3 point) Using a right tailed test, is the average battery life significantly greater than the claim of 32 hours? Explain.

Math   Statistics-And-Probability   
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