Question

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Q1 - 14 marks An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. Here are the data: Age 30-35 Less than 30 56 and older Total 20 40 100 In-Town Branch Mall Branch Total 40 20 30 50 100 50 90 60 200 Show your work for the questions that require calculations. a) What is the null hyposthesis? b) What type of test is this? c) What are the expected numbers for each cell if the null hypothesis is true? d) Find the X? statistic. e) How many degrees of freedom does it have? f) Find the P-value. g) What do you conclude?

Answer 1

Answer:-

Given That:-

Customer ages An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at the branch located near the mall.

a) Whatis the null hypothesis?

Null hypothesis: The age distribution of customers in the town is the same as the age distribution of customers in the mall.

H.

b) What type of test is this?

The Chi-square test of Independence

c) What are the expected numbers for each cell if the null hypothesis is true?

The expected numbers of each cell are got as follows:

	Less than 30	30 - 55	56 or order	Total
In-Town branch	50 * 100 /200 = 25	90* 100/200 = 45	60 * 100/200 = 30	100
Mall branch	50*100/200 = 25	90* 100/200 = 45	60 * 100/200 = 30	100
Total	50	90	60	200

d) Find the $\chi^2$ statistic?

The $\chi^2$ statistic is got as follows:

Observed (O)	Expected (E)	$(O-E)^2/E$
20	25	1.00
40	45	0.56
40	30	3.33
30	25	1.00
50	45	0.56
20	30	3.33
Total = $\chi^2$ =		9.78

e) How many degrees of freedom does it have?

Degrees of freedom = (r - 1) x (c - 1)

= (2 - 1) x (3 - 1)

= 2

f) Find the p -value

By Technology p -value = 0.00753

g) What do you conclude?

Since p - value is less than $\alpha$ difference is significant.

Reject null Hypothesis.

Conslusion:

The data do not support the claim that the age distribution of customers in the town is the same as the age distribution of customers in the mall.

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