Question

A mechanical engineering lab was hired to test the distance travelled by a new design of Dunlop brand golf balls, when struck by a standardized mechanically-driven club. Over several months of production, 30 randomly selected golf balls were tested. The mean distance travelled by the balls in the sample was 369 yards, and the standard deviation was 8.4 yards. Studies of pro golfers and their results have shown that balls that reach 350 yards in this test (not more, not less) are correlated with the best performance during matches. Report answers for multiple choice as a single letter with no punctuation, i.e. A

(1) What would the lab's null hypothesis be? A. The golf ball will travel 350 yards. B. The golf ball will travel a distance different from 350 yards. (2) Find the normalized tobs t o b s score for the observed mean distance travelled by Titleist. Report 2 digits after the decimal. tobs= t o b s =

(3) Sketch a normalized t distribution (see the Practice Problems for examples), and add tobs t o b s on the plot of the null t t -distribution. Shade in the appropropriate region that represents the probability of a value as large or more extreme that tobs t obs , in either direction. (I.e. don't forget the other tail.) You next find that for this sample, tcrit=t0.05(2),df t c r i t = t 0.05 ( 2 ) , d f = 2.04. Add this value to your t t distribution plot. Which of the following graphs most resembles your sketch?

(4) Find the 95% confidence interval for the mean distance travelled by Dunlop golf balls when hit by the mechanical golf club. Report 1 digit after the decimal for each value. 95% confidence interval: \[,\]

(5) What statistical conclusion should the researchers arrive at from this study? A. Reject the Null Hypothesis. B. Fail to Reject the Null Hypothesis. C. Accept the Null Hypothesis.

(6) What more colloquial conclusion should the researchers arrive at from this study? A. Golf balls from this brand do not travel the 350 yard target distance. B. The data does not provide evidence that this brand's golf clubs produce a distance other than 350 yards. C. The brand's golf balls travel on average 350 yards. Previous Page Next Page

Answer 1

The provided sample mean is Xˉ=369 and the sample standard deviation is s=8.4, and the sample size is n=30.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 350

Ha: μ ≠ 350

This corresponds to a two-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 two-tailed test is tc​=2.045.

The rejection region for this two-tailed test is R={t:∣t∣>2.045}

(3) Test Statistics

The t-statistic is computed as follows:

t= 12.39

3) Decision about the null hypothesis

Since it is observed that ∣t∣=12.389>tc​=2.05, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0.00, and since p=0.000<0.05, it is concluded that the null hypothesis is rejected.

95% confidence interval is 365.9<μ<372.1

(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 different than 350, at the 0.05 significance level.

6) More colloquial conclusion should the researchers arrive at from this study is A. Golf balls from this brand do not travel the 350 yard target distance.