23. Comparing NFL Quarterbacks How does Alex Smith, quarterback for the Kansas City Chiefs, compare to Joe Flacco, quarterback for the Baltimore Ravens? The following table shows the number of completed passes for each athlete during the 2017 NFL football season

a. The TI-84 Plus analysis uses the pooled estimate of σ². Is the assumption of equal variances reasonable?
Why or why not?

b. Do the data indicate that there is a difference in the average number of completed passes for the two quarterbacks? Test using a 5.05.

c. What is the p-value for the test?

d. Use the information provided along with the pooled variance, s2 539.4115 to construct a 95% confidence interval for the difference in the average number of completed passes for the two quarterbacks. Does the confidence interval confirm your conclusion in part b? Explain.
24. An Archeological Find Twenty-six samples of Romano-British pottery, found at four different kiln sites in the United Kingdom,11 were analyzed to determine their chemical composition. The percentage of aluminum oxide in each of 10 samples at two sites is shown here.

Do the data provide sufficient information to indicate that there is a difference in the average percentage of aluminum oxide at the two sites? Test at the 5% level of significance.

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Alex Smith Joe Flacco 20 23 22222 25 27 29 23 25 14 19 25 19 22628 25 27 16 21 23 222222 22 19 29 34 31 26 10 8 20 27 25 24 9 20