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.

Alex SmithJoe Flacco2527292522192325272934312014162610819252120272523192823249202-SampTTest₁₂t = 0.3250234901p = 0.7474965338df = 29x1

= 22.73333333x2

= 22Sx1

= 4.463609473Sx2

= 7.589466384

(a)

TheTI-84 Plusanalysis uses the pooled estimate of².

Is the assumption of equal variances reasonable? Why or why not?

Yes, because the ratio of the larger variance to smaller variance is less than 3.

Yes, because the ratio of the larger variance to smaller variance is more than 3.

No, because the ratio of the larger variance to smaller variance is not equal to 1.

No, because the ratio of the larger variance to smaller variance is less than 3.

No, because the ratio of the larger variance to smaller variance is more than 3.

(b)

Do the data indicate that there is a difference in the average number of completed passes for the two quarterbacks? Test using= 0.05.(Use₁for the population mean for Alex Smith and₂for the population mean for Joe Flacco.)

State the null and alternative hypotheses.

H₀: (₁₂) < 0 versusH_a: (₁₂) > 0

H₀: (₁₂)0 versusH_a: (₁₂) = 0

H₀: (₁₂) = 0 versusH_a: (₁₂) > 0

H₀: (₁₂) = 0 versusH_a: (₁₂)0

H₀: (₁₂) = 0 versusH_a: (₁₂) < 0

State the test statistic. (Round your answer to three decimal places.)

t=

State the rejection region. (If the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.)

t>t<

State the conclusion.

H₀is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.

H₀is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.

H₀is not rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.

H₀is rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco.

(c)

What is thep-value for the test? (Round your answer to three decimal places.)

p-value =

(d)

Use the information provided along with the pooled variance,s²= 39.4115

to construct a 95% confidence interval for the difference in the average number of completed passes for the two quarterbacks. (Round your answers to three decimal places.)

passes topasses

Does the confidence interval confirm your conclusion in part (b)? Explain.

No, since (₁₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.

No, since (₁₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.

Yes, since (₁₂) = 0 is in the interval, there is insufficient evidence to indicate that there is a difference in the means.

Yes, since (₁₂) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means.

Yes, since (₁₂) = 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.

You may need to use the appropriateappendix tableortechnologyto answer this question.