Question

Context:

Are males more likely to purchase fried products than females? You record the gender of all the customers for one week and find the following:

	Purchased Fried Product	Did NOT Purchase Fried Product	Total
Male	42	33	75
Female	38	43	81
Total	80	76	156

At the 0.05 level of significance, is there evidence that there is a difference in the distribution of sales of fried products between males and females. Use Excel to calculate your answers below.

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1a) Which test will you use to determine if there is a difference in distribution?

a) One sample hypothesis test

b)Two sample hypothesis test

c) One way ANOVA

d) Two way ANOVA

e) Chi-square

f) Correlation

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1b) What value did you calculate for your test statistic (t-value, z-value, f-value or chi-value)?

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1c) What value did you calculate for your critical value?

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1d) What value did you calculate for your p-value?

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1e) Which of the following best describes what you would conclude from these calculations?

a) There is no difference in the distribution of males and females the purchase fried products.

b) Males are more likely to purchase fried products.

c) Females are more likely to purchase fried products.

d) There is a difference in the distribution of males and females that purchase fried products.

Thanks for your help.

Answer 1

To find out if there is evidence that there is a difference in the distribution of sales of fried products between males and females, we will conduct a chi-square test. The correct option is e)

The formula is:

To find out the expected values, we have to multiply the corresponding row total and column total, divide it by the overall total. The calculation table is:

Oi	Ei	(Oi-Ei)^2/Ei
42	38.46	0.325835
38	41.54	0.301675
33	36.54	0.342956
43	39.46	0.317577
	Total	1.29

1b) Chi-square statistic = 1.29

1c) Critical value of chi-square at df = (2-1)*(2-1) = 1 is 3.84

1d) P-value is 0.2560 (from the table)

1e) We fail to reject the null hypothesis. We conclude that there is no difference in the distribution of males and females the purchase fried products.

A) is correct