1. Listed below are baseball team statistics, consisting of the proportions of wins and the result of this difference: Difference (number of runs scored) - (number of runs allowed). The statistics are from a recent year, and the teams are NY—Yankees, Toronto, Boston, Cleveland, Texas, Houston, San Francisco, and Kansas City.
Construct a scatter plot, find the value of the linear correlation coefficient r, and find the critical values of r from Table VI, Appendix A, p. A-14, of your textbook Elementary Statistics.
Use α = 0.05.
Is there sufficient evidence to conclude that there is a linear correlation between the proportion of wins and the above difference?
The null hypothesis is = 0 which shows the linear correlation is not significant.
The alternative hypothesis where it is using the p-value: p-value =2p(t>test statistic) =2p(t>3.9833) =2[1-p(t 3.9833)] =2(0.005248) =0.010496
Clearly this shows that the p-value is less than 0.05 which shows the linear relationship is not significant.
3. Given below is a control chart for the temperature of a freezer unit in a restaurant. The owner of the restaurant is deciding whether or not to buy a new unit. The two charts display the temperature for the past two weeks. Write a paragraph analyzing the control charts and argue whether the owner should buy a new unit or not. (5-6 sentences).
I would counsel the owner to purchase the new unit. The two charts below show a large variation in temperatures. When storing food for freshness large variations in temperature over time can allow bacteria growth and cause food spoilage. The large warm spike in week 2 is particularly concerning. As a restaurant owner I would not trust the food stored under these conditions nor would I risk serving it to my customers.