Question

The mean throwing distance of a football by Marco, a high school freshman quarterback, is 40 yards. The team coach tells Marco to adjust his grip to get more distance. The coach records the distances for 20 throws. For the 20 throws, the mean distance was 45 yards with a standard error of 0.44 yards. The coach thought the different grip helped Marco throw farther than 40 yards. Conduct a hypothesis test using α = 0.05 as the significance level. H0: H: Sample Statistic = null value = SE = Z statistic = Test type = p-value = Decision =

Answer 1

Given : sample size=n=20

sample mean=$\bar{X}=40$

standard error=SE=0.44

significance level=

= 0,05

Hypothesis : $H_0:\mu=40$ Vs $H_a:\mu\neq 40$

The test statistic is ,

$t_{stat}=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}=\frac{\bar{X}-\mu_0}{SE}=\frac{45-40}{0.44}=11.3636$

The p-value is ,

p-value=$P(t_{d.f.}>|t_{stat}|)=P(t_{20-1}>11.3636)=0.0000$

The Excel function is , =TDIST(11.3636,19,2)

Decision : Here , p-value=0.0000<

= 0,05

Therefore , reject Ho.

Conclusion : Hence , there issufficient evidence to support the claim that the coach thought the different grip helped Marco throw farther than 40 yards.