Directions: Show all steps of your work for each of the problems below. Clearly indicate your
final answer. For questions that require calculations, all calculations should be shown, not just the final answer. For questions that require an answer using software, graphs or output tables should be copied and pasted into your exam, with suitable discussion. You should be able to use the Symbol inserter in Word for any symbols you would need. All work must included in the pdf file.
1. Your consulting group has been hired as political pollsters for the upcoming election. Your job is to
estimate the proportion of voters who will vote for the Democratic ticket. You want to be 90%
confident that your prediction is within 0.04 of the actual population proportion.
a.) In order to achieve this, what sample size is needed?
b.) Suppose your fickle employers now want to have 95% confidence. What sample size will be
c.) They have changed their mind once more and now, along with 95% confidence, they want to
know the sample size needed with a margin of error of 0.03. What sample size is needed?
d.) Based on your answers to these first three questions, what general conclusions can be drawn
about how both the confidence level and margin of error affect the sample size needed, as well
as how they interact with each other?
e.) Assuming that it will cost your organization roughly $1 for each person you survey and you
have a total of $250,000 to spend, what sampling plan in terms of confidence level, margin of
error, and sample size would you recommend to management, and why? Please be as specific
and quantitative as possible and be sure to justify your statements.
2. Zagat’s publishes restaurant and hotel ratings for various establishments all over the world. The
Excel file, Zagat Ratings, contains the ratings for food, décor, service, and price per person for a
sampling of 50 restaurants located in New York City and 50 located in Long Island. Your group has
been asked by Mr. Zagat himself to develop a regression model to predict the average price per
person based on the sum of the ratings for food, décor and service. For this question, you must use
software for the calculations. Please use the attached data set.
a.) Set up a scatter diagram with the summated ratings on the horizontal axis and price per
person on the vertical axis.
b.) Assuming a linear relationship, use the least-squares method to find the regression equation
and the coefficients b0 (intercept) and b1 (slope) and interpret their values.
c.) Use the regression equation from part b) to predict the average price of a restaurant with a
summated rating of 50. You may do this one without software if you like.
d.) Remember that the computed value of the slope is a sample-based estimate of the unknown
actual slope. Compute a 95% confidence interval estimate of the actual slope,.
e.) Compute the coefficient of determination and interpret its meaning.
f.) Perform a simple residual analysis on your results to determine the adequacy of the fit – the
appropriateness, if you will - of the linear model. You will need to plot the errors
(difference between actual and predicted y-values) and determine to what extent they are
independent of the x-values.
g.) At the 0.05 level of significance, is there evidence of a linear relationship between the price
per person and the summated ratings?
h.) How useful do you think the summated rating is as a predictor of price per person? Explain.
3. Listed below are the Flesch Reading Ease scores (higher scores mean the material is easier to read)
from each of 12 randomly selected pages from three books, one each by Tom Clancy, JK Rowling
and Tolstoy. Use software with a .05 significance level to test the claim that the three books have
the same mean score, and then perform Bonferroni’s post-hoc test. Interpret the results and explain
whether or not the books appear to be at the same reading level.
Clancy 58.2 73.4 73.1 64.4 72.7 89.2 43.9 76.3 76.4 78.9 69.4 72.9
Rowling 85.3 84.3 79.5 82.5 80.2 84.6 79.2 70.9 78.6 86.2 74.0 83.7
Tolstoy 69.4 64.2 71.4 71.6 68.5 51.9 72.2 74.4 52.8 58.4 65.4 73.6
|Due By (Pacific Time)||05/16/2014 08:00 pm|
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