Description:
Finish the attached two page pdf.
Question 1
A hotel wants to determine a 99% confidence interval for the average daily occupancy of its rooms. It wants the interval to be no more than plus or minus 5 room.
a) How many days should be sampled to construct this interval if σ=12 rooms per day?
b) How many days should be sampled to construct this interval if σ=10 rooms per day?
c) In 30 words or less, explain why the number of days changes from part 1 to part b.
Question 2
Suppose the FDA receives complaints that Pepsi is not putting 2000 ml of soda in its two liter bottles. If the claim is true, the FDA will fine Pepsi. To test the claim, the FDA selects a random sample of 64 two-liter bottles of Pepsi and measures their volume. This data provides a sample mean of 1994 ml and a sample standard deviation of 32 ml. Recognize that even if some change that the FDA's random sample will produce a sample mean is less from 2000 ml; rather the FDA must use statistics and determine how many standard deviations 1994 is from 2000, assuming Pepsi actually does put 2000 ml into each bottle on average. Notice that statistical testing gives the benefit of the doubt to Pepsi. Letting μ be the amount of product Pepsi puts into each two-liter bottle on average, the FDA's hypotheses are
H0: μ = 2000
Ha: μ ≠ 2000
Notice that the FDA will never conclude that μ = 2000, but rather it may simply fail to reject that μ is equal to 2000.
a) Is there statistical evidence to fine Pepsi? Suppose the FDA's wants to test the claim with 95% confidence.
b) Suppose the FDA increases its standard to 99% confidence. Test the null hypothesis at the 1 percent significance level.
Question 3
The college bookstore tells prospective students that the average cost if its textbooks is $52 with a standard deviation of $4.50. A group of smart statistics students thinks that the average cost is more than $52. In order to test the bookstore's claim against their alternative, the student will select a random sample of 100 students. Assume that the mean from their random sample is $52.80. Test the hypothesis at the 5% level of significance and state your decision.
Question 4
A social justice activist group believes a particular judge imposes sentences, not in line with the standard practices. In particular, it is well accepted that the average sentence should be 5 years. The activist group collect data on 75 different cases for the judge in question. The data reveals a sample mean of 7.2 years with a sample standard deviation of 3.8 years. The activist group wants to test if the judge's average sentence is in line with standard practice. Thus. the hypotheses the group has in mind are:
H0: μ=5
H0: μ≠5
The activist group is willing to use 90% confidence interval to test the null hypothesis against the alternative hypothesis. Carry out the test. What is the conclusion?
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