Instructions: Read this very carefully. In one Excel file create two sheets. Label one sheet
“Problem 1” and label the second sheet “Problem 2.” Your solutions to the two problems should
be recorded on the corresponding sheet. Additionally, you should clearly label each part of the
problems with (a), (b), etc., and every computation should be labeled. For example, in the cell
next to the mean of the data, you should have typed the word mean or average.
Be sure to do your computations using Excel. Do not do computations using Table A or on a
calculator and then type the answers into Excel.
1. Breast-feeding mothers secrete calcium into their milk. Some of the calcium may come from
their bones, so mothers may lose bone mineral. Previous research shows that the average
percent change in mineral content for breast-feeding mothers is µ = -4% with standard deviation
s = 2.5%. Researchers suspect that mothers who drink at least 8 ounces of milk per day
while breastfeeding (milk-drinking mothers) lose less bone mineral. They measured the percent
change in mineral content of the spines of 47 milk-drinking mothers during three months
of breastfeeding. The data is contained in the Excel file that accompanies this worksheet.
(a) (4 points) Make a histogram of the data (use class sizes of 1.5 or 2) to see that they
appear to follow an approximately Normal distribution.
(b) (4 points) Consider the question: Do milk-drinking mothers lose less bone mineral than
all breast-feeding mothers? State the null and alternative hypotheses in terms of mean
percent change µ in mineral content.
(c) (4 points) Find the z test statistic.
(d) (4 points) What is the P-value for your z?
(e) (4 points) What do you conclude about the population of milk-drinking mothers?
2. Most professional athletes will agree that resources (money, equipment, etc.) matter when it
comes to success in sports. One way to measure a country’s success in sports would be to
count the total number of medals won by athletes from a country in the Olympics. We know
that the average number of medals won by countries in the 2012 Summer Olympics was 11.4.
Countries not classified as first world countries have fewer resources to aid in the training of
their athletes. A random sample of countries with fewer resources was chosen and the total
medal count from the 2012 Summer Olympics was recorded.
(a) (4 points) Consider the question: Do countries with fewer resources win fewer medals
in the Olympics? State the null and alternative hypotheses relative to this question.
(b) (4 points) Find the t test statistic.
(c) (4 points) What is the P-value for your t?
(d) (4 points) Is the data significant at significance level a = 0.05?