Question

Use the contingency table to the right to complete parts? (a) through? (c) below.		A	B	Total
	1	1313	3737	5050
	2	3737	3838	7575
	Total	5050	7575	125125

a. Find the expected frequency for each cell.

	A	B	Total
1	2020	3030	5050
2	3030	4545	7575
Total	5050	7575	125125

?(Type integers or? decimals.)

b. Compare the observed and expected frequencies for each cell.

Choose the correct answer below.

A.

The totals for the observed values are always greater than the totals for the expected values.

B.

The totals for the observed and expected frequencies are the same.

C.

The expected values are always greater than the observed values.

D.

The observed values are always greater than the expected values.

c. Compute

chi Subscript STAT Superscript 2?2STAT.

Is it significant at

alpha?equals=0.050.05??

First let

pi?1

be the proportion of all events of interest in? A, and let

pi?2

be the proportion of all events of interest in B. Determine the hypotheses. Choose the correct answer below.

A.

Upper H 0 : pi 1 equals pi 2H0: ?1=?2

Upper H 1 : pi 1 not equals pi 2H1: ?1??2

B.

Upper H 0 : pi 1 greater than or equals pi 2H0: ?1??2

Upper H 1 : pi 1 less than pi 2H1: ?1<?2

C.

Upper H 0 : pi 1 not equals pi 2H0: ?1??2

Upper H 1 : pi 1 equals pi 2H1: ?1=?2

D.

Upper H 0 : pi 1 less than or equals pi 2H0: ?1??2

Upper H 1 : pi 1 greater than pi 2H1: ?1>?2

Calculate the test statistic.

chi Subscript STAT Superscript 2?2STATequals=nothing

?(Round to two decimal places as? needed.)

What is the? p-value?

?p-valueequals=nothing

?(Round to three decimal places as? needed.)Is this value significant at

alpha?equals=0.050.05??

A.

YesYes?,

because the? p-value is

less than or equal toless than or equal to

the alpha level.? Therefore, the null hypothesis should not be rejected.not be rejected.

B.

YesYes?,

because the? p-value is

less than or equal toless than or equal to

the alpha level.? Therefore, the null hypothesis should be rejected.be rejected.

C.

NoNo?,

because the? p-value is

greater thangreater than

the alpha level.? Therefore, the null hypothesis should not be rejected.not be rejected.

D.

NoNo?,

because the? p-value is

greater thangreater than

the alpha level.? Therefore, the null hypothesis should be rejected.be rejected.

Answer 1

a) as expected frequency =row total*column total/grand total

Expected	Ei=?row*?column/?total	A	B	Total
	1	20.000	30.000	50
	2	30.000	45.000	75
	Total	50	75	125

b)

B.

The totals for the observed and expected frequencies are the same.

c)

A.

Upper H 0 : pi 1 equals pi 2H0: ?1=?2

Upper H 1 : pi 1 not equals pi 2H1: ?1??2

applying chi square test:

chi square	=(Oi-Ei)2/Ei	A	B	Total
	1	2.45	1.63	4.08
	2	1.63	1.089	2.72
	Total	4.08	2.72	6.806

  test statistic =6.81

p value =0.0091

option B:Yes?, because the? p-value is less than or equal to the alpha level.? Therefore, the null hypothesis should be rejected.