Introduction to Statistical Analysis
Directions: Show all steps of your work for each of the problems below.
Clearly indicate your final answer.
As the director of membership for a nationally renowned art museum, it is your job
to increase the number of members and the quality of the membership experience.
You’ve been wonderfully successful in recent years—membership has reached well
into the thousands. You have also recently made a greater push for dataâ€driven
decisionâ€making regarding membership strategies. As such, you have begun more
systematically collecting and rigorously analyzing data.
Of your 7,120 members, you know the following:
•59% are women
•Of the women, 62% have income equal to or less than $100,000
•Of the men, 45% have income equal to or less than $100,000
•Of the women, 72% are married
•Of the men, 86% are married
1. How many members are married men?
2. If you were to select a member at random, what are the chances that this member
would have income greater than $100,000?
3. Of those who make more than $100,000, what percentage is female?
Assume that your members’annual income is normally distributed with mean =
$89,000 and standard deviation = $17,000.
4. What is the likelihood that a member, selected at random, makes at least
Interested in how your membership demographics compare to the membership of
the local opera company, you are able to obtain a random sample of 15 opera house
members. Coincidentally, you happen to know that the income for all opera
members is also normally distributed with a standard deviation of $23,000. The
mean income from the 15 randomly sampled members equals $110,000.
5. Is the mean income of art museum members within the 95% confidence interval
of mean income of the opera house members? Based on that answer, would you
informally accept or reject the hypothesis that the mean incomes of the two
populations are equal?
6. Assume for this question that the sample of 15 opera house members was not, in
fact, random as described in question 5. Rather, assume that the 15 individuals for
whom you have income data were the first 15 who responded to an opera house email
survey that promised a $50 Amazon.com gift card to the first 15 respondents.
How might the nature of this sample affect your answer to question 5?
7. Nine months ago, the director of a local health clinic implemented a new prenatal
outreach program designed to increase the number of prenatal clinic visits among
pregnant women served by the clinic. Before the program, the average number of
prenatal visits for women was 2.7. The director wants to evaluate the success of the
new program, so she obtained data on 32 women who delivered babies in the most
recent month. The distribution of number of visits for this group was:
# Prenatal Visits % of women with # of visits
a) Find the average and standard deviation of the number of visits for the 32
b) Find the 90% confidence interval and 95% confidence interval for the mean
number of visits for women under the new program. In one or two brief sentences,
what tradeâ€off is illustrated by the two intervals?
c) Based on your calculations above, is the program effective at increasing the
number of visits? Explain.
|Due By (Pacific Time)||04/25/2014 11:00 pm|
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