Question

An advertising firm has decided to ask 93 customers at each of four local shopping malls if they are willing to take part in a market research survey. At αα = 0.10 is there evidence to show that the proportions are not all the same.

	A	B	C	D
Willing	67	68	69	70
Not Willing	26	25	24	23

What are the expected numbers? (round to 3 decimal places)

	A	B	C	D
Willing
Not Willing

The hypotheses are

  H0:pA=pB=pC=pDH0:pA=pB=pC=pD

HA:HA: At least one of the proportions is different. (claim)

Since αα = 0.10 the critical value is 6.251

The test value is: (round to 3 decimal places)

The p-value is (round to 3 decimal places)

So the decision is to

• do not reject H0H0
• reject H0H0

Thus the final conclusion is

• There is enough evidence to support the claim that at least one of the proportions is different.
• There is enough evidence to reject the claim that at least one of the proportions is different.
• There is not enough evidence to support the claim that at least one of the proportions is different.
• There is not enough evidence to reject the claim that at least one of the proportions is different.

Answer 1

Expected numbers for each cell are,

Eij = (Row i Total) * (Column j total) / Grand Total

	A	B	C	D	Total
Willing	(274 * 93)/372 = 68.5	(274 * 93)/372 = 68.5	(274 * 93)/372 = 68.5	(274 * 93)/372 = 68.5	274
No Willing	(98 * 93)/372 = 24.5	(98 * 93)/372 = 24.5	(98 * 93)/372 = 24.5	(98 * 93)/372 = 24.5	98
Total	93	93	93	93	372

The test value is  

where fo and fe are the observed and expected frequencies respectively.

= 0.277

Degree of freedom = (r - 1) * (c - 1) = (2 - 1) * (4 - 1) = 3

P-value = P( > 0.277, df = 3) = 0.964

Since p-value is greater than the significance level of 0.05,

• do not reject H0

Thus the final conclusion is

• There is not enough evidence to support the claim that at least one of the proportions is different.