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Use the contingency table to the right to complete parts? (a) through? (c) below

ID: 3369096 • Letter: U

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.

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

Explanation / Answer

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

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:

  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.

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