Question

11. Sales (measured by number of boxes sold with 12 balls in each box) of six different brands of golf balls at a retail store were recorded for one month. The observed (absolute) frequencies and expected (absolute) frequencies as well as the MegaStat results of a χ²(Chi-square) Goodness of Fit test appear below.

observed expected

Brand 1: Bridgestone	131	200
Brand 2: Callaway	273	200
Brand 3: Nike	119	200
Brand 4: Srixon	301	200
Brand 5: Titleist	176	200
Brand 6: Wilson	200	200
total	1200	1200
	137.14	chi-square
	5	df
	7.25E-28	p-value

1. (3 pts) Write out the Ho for this Goodness of Fit test.

2. (4 pts.) Interpret the results (for α = .05). Can we reject Ho? Explain.

Answer 1

(a)

Ho: The proportion of boxes sold are equal for all 6 brands. i.e. 1/6

Pbridgestone = 1/6, Pcallaway = 1/6, Pnike = 1/6, Psrixon = 1/6, Ptitlesit = 1/6, Pwilson = 1/6

Ha: Some of the population proportions differ from the values stated in the null hypothesis

This corresponds to a Chi-Square test for Goodness of Fit.

(b)

$\chi^{2}$ = 137.14

$\chi^{2}$ critical = 11.070

As $\chi^{2}$ (137.14) is greater than $\chi^{2}$ critical, we reject the Null hypothesis.

Also as the p value ( 7.25E-28) is less than $\alpha$ (0.05) we reject the Null hypothesis.

Hence we have sufficient evidence to believe some of the population proportions differ from the values stated in the null hypothesis.