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DSME 5510  Quantitative Analysis for Decision Making

Individual Assignment

Due Date: 15 November 2023 (Wed), 5 p.m.

1. Caring for hospital patients

Any medical item used in the care of hospital patients is called a factor. For example, factors can be intravenous tubing, intravenous fluid, needles, shave kits, bedpans, diapers, dressings, medications, and even code carts.

The coronary care unit at Bayonet Point Hospital (St. Petersburg, Florida) investigated the relationship between the number of factors per patient, x, and the patient's length of stay (in days), y. The data for a random sample of 50 coronary care patients are given in the Excel tab named Q2 FACTORS.

(a) Construct a scatterplot of the data.

(b) Find the least squares line for the data and plot it on your scatterplot.

(c) Define β1 in the context of this problem.

(d) Test the hypothesis that the number of factors per patient (x) contributes no information for the prediction of the patient's length of stay (y) when a linear model is used (use α = .05). Draw the appropriate conclusions.

(e) Find a 95% confidence interval for β1 . Interpret your results.

(f) Find the coefficient of determination for the linear model you constructed in part b. Interpret your result.

2. Simpson’s Paradox

Western University has only one women’s softball scholarship remaining for the coming year.  The final two players that Western is considering are Allison Fealey and Emily Janson.  The coaching staff has concluded that the speed and defensive skills are virtually identical for the two players, and that the final decision will be based on which player has the best batting average.  Crosstabulations of each player’s batting performance in their junior and senior years of high school are as follows:

A player’s batting average is computed by dividing the number of hits a player has by the total number of at-bats. Batting averages are represented as a decimal number with three places after the decimal.

a. Calculate the batting average for each player in her junior year.  Then calculate the batting average of each player in her senior year.  Using this analysis, which player should be awarded the scholarship?  Explain.

b. Combine or aggregate the data for the junior and senior years into one Crosstabulations as follows:

Calculate each player’s batting average for the combined two years.  Using the analysis, which player should be awarded the scholarship?  Explain.

c. Are the recommendations you made in part (a) and (b) consistent?  Explain any apparent inconsistencies.

3. Binomial Distribution

According to a survey, one out of four investors in the United States has exchange-traded funds in their portfolios (USA Today, 11 January 2007).  Consider a random sample of 20 investors drawn from the US population.

a. Compute the probability that at least 2 investors have exchange-traded funds in their portfolios.

b. If you found that exactly 12 investors have exchange-traded funds in their portfolios, would you doubt the accuracy of the survey results?

c. Compute the expected number of investors who have exchange-traded funds in their portfolios.

4. Hypothesis Tests

A recent article concerning bullish and bearish sentiment about the stock market reported that 41% of investors responding to an American Institute of Individual Investors (AAII) poll were bullish on the market and 26% were bearish (USA Today, January 11, 2010). The article also reported that the long-term average measure of bullishness is .39. Suppose the AAII poll used a sample size of 450. Using .39 (the long-term average) as the population proportion of investors who are bullish, conduct a hypothesis test to determine if the current proportion of investors who are bullish is significantly greater than the long-term average proportion.

a. State the appropriate hypotheses for your significance test.

b. Use the sample results to compute the test statistics and the p-value.

c. Using α = .10, what is your conclusion?