A grocer wishes to determine if his costumers have preferred days of the week th

Question

A grocer wishes to determine if his costumers have preferred days of the week that they shop at his market. He randomly samples 105 from his customer data base and ask them which day of the week do they shop for groceries. The following table is the result of the survey. You will run a goodness of fit test and test at significance level of 5%. a. State the null and alternative hypothesis, alpha, degrees of freedom and finally the Chi Square critical value. b. Provide the "expected" table where the grocer felt the proportion of shoppers each day was the same.

Explanation / Answer

1.a

Null Hypothesis : H0 : Customers don't have preferred days to shop at market.

ALternative Hypothesis : Ha : Customers have specific preferred days to shop at market.

Alpha = 0.05

degrees of freedom = (7-1) = 6

CHi square critical value X2 critical= 12.592

b.

X2 = 5.60

so here X2 <  X2 critical so we cannot reject the null hypothesis and can conclude that Customers don't have preferred days to shop at market.

Observed (Oi) Expected (Ei) (oi -Ei) (Oi - Ei)^2 (Oi- Ei)^2/Ei M 10 15 -5 25 1.67 T 15 15 0 0 0.00 W 14 15 -1 1 0.07 th 16 15 1 1 0.07 F 11 15 -4 16 1.07 S 20 15 5 25 1.67 S 19 15 4 16 1.07 sum 5.60

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