Statistics

1) Hypothesis testing

As you possibly could have predicted, it was inevitable that the world of Reality TV would eventually find a way to penetrate the Game Show genre. A primary example is ‘Wipeout’, where the complex competitive events are now intertwined with expansive self-exploitation and antics. You are starting to believe that the producers are intentionally making the events easier to allow competitors additional air time. Looking back at the last season, you find that on average, the overall event time per individual is 17 min. This season, the first 5 competitors lasted 21 minutes into the competition with a standard deviation of 2.2 minutes. Based on this information, are Wipeout competitors lasting longer before dropping out this year as opposed to the previous 6 seasons? Use a level of significance of 0.01.

2) Hypothesis Testing

A machine is designed to fill jars with 16 ounces of coffee. A consumer suspects that the machine is not filling the jars completely. A sample of 35 jars has a mean of 15.8 ounces and a standard deviation of 0.6 ounces. At α=0.10, would you reject or accept the consumer’s claim?

3) Curve Fitting and Data Analysis

Perform a curve-fit analysis on the following data using Excel. Attempt different curve fits (linear regression, polynomial, etc). Briefly discuss which fit you think accurately reflects the data and why, include the correlation coefficients and residuals in your discussion.

4) Curve fitting and data analysis (covariance)

A process engineer is conducting a study of a stirred tank reactor system and has recorded the following data.

With a lack of first principal models of the system, the engineer wants to find the variable relationships empirically. Compare each set of data against all the others and analyze the results to see if any relationships exist, and the strength of these relationships. This is an open ended question, so the focus is on justifying your analysis.

5) Curve fitting and goodness of fit

In your continuing quest to thwart the Squirrel Armageddon you run simulations that will reduce the squirrel population (humanely). You place a pile of Arby’s at the alley between Lowes and Kiefaber and measure the number of squirrels lumbering to partake of the food versus time. After a few trials, you average the number of squirrels at each time and the results are as follows.

a) First, use Excel to plot and fit trendlines to the data. Do any of the fits make sense? Do any fits have an acceptable correlation coefficient (R2 > 0.96)?

b) You have found that the data may follow a trend according to the following equation.

Use this equation to perform a least squares regression on the data. (Use solver in Excel as we did in class to find the values for A, B, and C.) Plot this correlation on the plot from part a)

c) Calculate the correlation coefficient and compare it with the best fit for the Excel trends (from part a).