Question

Hypothesis Testing – Indicate five steps in your answers (Null/alternate hypotheses, test-statistic, rejection area, decision for rejection, conclusion)

Randy is a famous pitcher in Long Island High School. His average throwing distance is 35 yards. However, his coach was analyzing Randy’s throwing angle and figuring how he had a bad habit to unconsciously lift his arm earlier than he was supposed to do. Coach trained Randy for his new strategy and measured his throwing distance that turned out to be 38 yards after 11 throws with a sample standard deviation of 5.2 yards. Coach is now believing that his new strategy is effective making Randy throw farther than 35 yards. Are these data providing sufficient evidence, at the 5% of level of significance, to conclude that coach’s strategy is effective? (throwing distances follows normal distribution)

Answer 1

The provided sample mean is 38 and the sample standard deviation is s = 5.2, and the sample size is n = 11

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Null hypothesis:  coach’s strategy is not effective and his average throwing distance is 35 yards

Ho: μ = 35

Alternate hypothesis : coach’s strategy is effective and his average throwing distance is more than 35 yards

Ha: μ > 35

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is t_c = 1.812

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t = 1.913 >tc​=1.812, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p = 0.0424, and since p = 0.0424 <0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 35, at the 0.05 significance level.

Hence, coach’s strategy is effective and his average throwing distance is more than 35 yards