Question

The manager of a Farmer John Super Market would like to know if there is a preference for the day of the week on which customers do their shopping. A sample of 420 families revealed the following. At he 0.05 significance level, is there a difference in the proportion of customers that prefer each day of the week?

Days of the week	Number of persons
Monday	20
Tuesday	30
Wednesday	20
Thursday	60
Friday	80
Saturday	130
Sunday	80

a. State the null and alternate hypothesis.

b. State the decision rule.

c. Compute the value of the test statistic.

Days of week
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Total

d. What is your decision regarding the null hypothesis? Interpret the result.

Answer 1

The manager of a Farmer John Super Market would like to know if there is a preference for the day of the week on which customers do their shopping. A sample of 420 families revealed the following. At he 0.05 significance level, is there a difference in the proportion of customers that prefer each day of the week?

a. State the null and alternate hypothesis.

Ho: proportion of customers that prefer each day of the week is same

H1: proportion of customers that prefer each day of the week is different

b. State the decision rule.

Critical chi square with 6 df at 0.05 level =12.592

Rejection Rule: Reject Ho if calculated chi square > 12.592

c. Compute the value of the test statistic.

Goodness of Fit Test
	observed	expected	O - E	(O - E)² / E	% of chisq
	20	60.000	-40.000	26.667	16.33
	30	60.000	-30.000	15.000	9.18
	20	60.000	-40.000	26.667	16.33
	60	60.000	0.000	0.000	0.00
	80	60.000	20.000	6.667	4.08
	130	60.000	70.000	81.667	50.00
	80	60.000	20.000	6.667	4.08
Total	420	420.000	0.000	163.333	100.00
	163.333	chi-square
	6	df
	0.0000	p-value

d. What is your decision regarding the null hypothesis? Interpret the result.

calculated chi square = 163.33 which is > 12.592. we reject Ho.

We conclude that there is a difference in the proportion of customers that prefer each day of the week.