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

$120,000?

Part 2

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

1 15.6%

2 21.9%

3 28.1%

4 25.0%

5 9.4%

a) Find the average and standard deviation of the number of visits for the 32

women.

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.

Subject | Mathematics |

Due By (Pacific Time) | 04/25/2014 11:00 pm |

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