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. 2.
Difference
163
55
-5
88
51
16
-214
Wins
0.599
0.537
0.531
0.481
0.494
0.506
0.383
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).
The Essay on Inferential Statistics
With inferential statistics, you are trying to reach conclusions that extend beyond the immediate data alone. For instance, we use inferential statistics to try to infer from the sample data what the population might think. Or, we use inferential statistics to make judgments of the probability that an observed difference between groups is a dependable one or one that might have happened by chance ...
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.
