solve for d only **Statistical Analysis of Quarterback Performance**The analysis involves a comparison of the average number of completed passes between two quarterbacks, Alex Smith and Joe Flacco, using statistical methods.### (a) Assumption of Equal VariancesThe TI-84 Plus analysis uses the pooled estimate of σ². Consider whether the assumption of equal variances is reasonable:- **Answer**: Yes, because the ratio of the larger variance to the smaller variance is less than 3 (selected option).### (b) Hypothesis TestingDo the data indicate that there is a difference in the average number of completed passes for the quarterbacks?- **Null and Alternative Hypotheses**: - **\(H_0\)**: \(\mu_1 - \mu_2 = 0\) versus \(H_3\): \(\mu_1 - \mu_2 \neq 0\) (selected option)- **Test Statistic**: - \(t = 0.325\)- **Rejection Region**: - \(t \geq 2.045\) - \(t \leq -2.045\)- **Conclusion**: - \(H_0\) is not rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco (selected option).### (c) p-value for the Test- **p-value**: 0.747### (d) Confidence Interval ConstructionUsing pooled variance \(s^2 = 39.4115\), construct a 95% confidence interval for the difference:- **Does the confidence interval confirm your conclusion?**: - Yes, since \( (\mu_1 - \mu_2) = 0 \) is in the interval, there is insufficient evidence to indicate a difference in means (selected option).This comprehensive statistical analysis provides a deep dive into whether there is evidence of significant performance differences between the two quarterbacks based on their average completed passes. ### Comparing Quarterbacks: Alex Smith and Joe Flacco#### Completed Passes in the 2017 NFL SeasonThe following table shows the number of completed passes for each quarterback during the 2017 NFL football season.| **Alex Smith** | **Joe Flacco** ||----------------|----------------|| 25 | 22 || 29 | 29 || 27 | 19 || 23 | 16 || 28 | 20 || 25 | 19 || 23 | 24 || 29 | 21 || 22 | 20 |### Statistical AnalysisA **2-SampTTest** was conducted to compare the performance of the two quarterbacks.- Null Hypothesis (\(H_0\)): \(\mu_1 - \mu_2 = 0\)- Alternative Hypothesis (\(H_a\)): \(\mu_1 - \mu_2 \neq 0\)#### Test Results- **t** = 0.325- **p** = 0.747- Degrees of Freedom (df): 29- Sample Means: \(x_1 = 24\), \(x_2 = 22\)- Sample Standard Deviations: \(s_1 = 2.872\), \(s_2 = 3.698\)#### Assumption of Equal VariancesThe analysis uses the pooled estimate of \(s^2\). The assumption of equal variances is checked:- **Yes**, because the ratio of the larger variance to the smaller variance is less than 3.#### Conclusion of the Test- At a significance level (\(\alpha\)) of 0.05, **H_0 is not rejected**. - There is **insufficient evidence** to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco. This statistical analysis aids in understanding whether there is a significant difference between the performances of the quarterbacks based on completed passes during the season.

Given Data : For Sample 1 x̄1 = 22.73 n1= 15 s1= 4.4636 For Sample 2…

x2 = 22 Sxi = 4.463609473 Sx2 - 7.589466304 (a) The TI-84 Plus analysis uses the pooled estimate of o. Is the assumption of equal variances reasonable? Why or why not? O Yes, because the ratio of the larger variance to smaller variance is less than 3. O Yes, because the ratio of the larger variance to smaller variance is more than O No, because the ratio of the larger variance to smaller variance is not equal to 1. O No, because the ratio of the larger variance to smaller variance is less than 3. O 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 a = 0.05. (Use u, for the population mean for Alex Smith and l, for the population mean for Joe Flacco.) State the null and alternative hypotheses. O Ho: (H, - 2) = 0 versus H: (M, - H2) = 0 O Ho: (H, - Hg) = 0 versus H: (u, - H2) > 0 O Hạ: (H, - H) - o versus H: (H, - H2) < 0 O Ho: (H - H2) < o versus H: (u, - H2) > 0 O Ho: (H, - H2) * O versus H: (, - H2) - 0 State the test statistic. (Round your answer to three decimal places.) - (0.325 State the rejection region. (1f the test is one-tailed, enter NONE for the unused region. Round your answers to three decimal places.) :> 2.045 *< -2.045 State the conclusion. O H, is rejected. There is sufficient evidence to indicate that the average number completed passes is different for Alex Smith and Joe Flacco. O Ho is not rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco. O H, is not rejected. There is sufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco. O Ho is rejected. There is insufficient evidence to indicate that the average number of completed passes is different for Alex Smith and Joe Flacco. (c) What is the p-value for the test? (Round your answer to three decimal places.) p-value - 0.747 (d) Use the information provided along with the pooled variance, s = 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 to passes Does the confidence interval confirm your conclusion in part (b)? Explain. O No, since (, - uz) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means. O Yes, since (u, - Hg) = 0 is not in the interval, there is sufficient evidence to indicate that there is a difference in the means. O Yes, since (u, - Hg) = 0 is in the interval, there is insufficient evidence to indicate that there is a difference in the means. O No, since (H, - l,) = 0 i in the interval, there is sufficient evidence to indicate that there is a difference in the means. O Yes, since (u, - H,) - 0 is in the interval, there is sufficient evidence to indicate that there is a difference in the means.