Question

A golf association requires that golf balls have a diameter that is 1.68 inches. To determine if golf balls conform to the standard, a random sample of golf balls was selected. Their diameters are shown in the accompanying data table. Do the golf balls conform to the standards? Use the c = 0.05 level of significance. B Click First deter Data Table Golf Ball Diameter (inches) HP (Type inte Find the te 1683 1.686 1.676 1677 1685 1.682 1681 1.686 1.673 1.674 1.684 (Round to 685 Find the P Print Print Done Done Click to sell

Answer 1

Null and alternative hypothesis

Ho : $\mu$ = 1.68

H1 : $\mu$ $\neq$ 1.68

Test statistic  

t = (xbar - $\mu$ )/ (s/$\sqrt$n)

t = 1.681 - 1.680 / (0.005/$\sqrt$12)

t = 0.69

P-value for t = 0.69 and d.f = n -1 = 11 , two tailed test

p-value = 2*P(t > 0.69 ) d.f =11

p-value = 0.504

Decision rule : If p-value < a we reject the null hypothesis otherwise we fail to reject the null hypothesis.

Our p-value = 0.504 > 0.05 , Do not  reject Ho

conclusion : Do not reject Ho , There is not sufficient evidence to conclude that the golf balls do not conform to the associations standards at the a = 0.05 level of significance.