A study conducted in a certain period of time found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again. Suppose that the hiring intentions of the respondents were as follows:

• 32% selectedHire
• 29% selectedLikely to Hire
• 21% selectedHire Uncertain
• 18% selectedDo Not Hire

Six month later, a random sample of 100 employers were asked about their hiring intentions and gave the following responses:

• 29 selectedHire
• 35 selectedLikely to Hire
• 14 selectedHire Uncertain
• 22 selectedDo Not Hire

At 1% significance level, does it mean that proportions from the initial study have significantly changed?

Use Goodness-of-Fit test and

2

2

distribution.

For part (a), round your answers in the "(

O

E

)

2

E

(O-E)2E

" column to 3 decimal places.

(a) Fill in the table below.

Hiring Intention

ObservedFrequencyO

O

Expected FrequencyE

E

O

E

O-E

(

O

E

)

2

(O-E)2

(

O

E

)

2

E

(O-E)2E

Hire29Likely to Hire35Hire Uncertain14Do Not Hire

22Total

2

=

(

O

E

)

2

E

=

2=(O-E)2E=

(b) State the null and alternative hypotheses, and identify which one is the claim.

H

0

H0

:Select an answer

At least two of the frequencies stay the same.

At least one of the frequencies changes.

At least one of the frequencies stays the same.

All of the frequencies stay the same.

At most one of the frequencies changes.

H

1

H1

:Select an answer

At least one of the frequencies changes.

At most one of the frequencies changes.

At least one of the frequencies stays the same.

All of the frequencies stay the same.

At least two of the frequencies stay the same.

Which one is the claim?

• H
• 1
• H1
• H
• 0
• H0

(c) Enter the number of degrees of freedomd

f

=

df=

For part (d), round your answer to 3 decimal places.

(d) What is the critical value

2

c

r

=

cr2=

(e) Is the null hypothesis rejected? Is the alternative hypothesis supported?

• Fail to rejectH
• 0
• H0
• and fail to supportH
• 1
• H1
• (claim)
• RejectH
• 0
• H0
• and supportH
• 1
• H1
• (claim)
• RejectH
• 0
• H0
• (claim) and fail to supportH
• 1
• H1
• Fail to rejectH
• 0
• H0
• (claim) and supportH
• 1
• H1

(f) Select the correct statement.

• At 1% significance level, there is not sufficient sample evidence to support the claim that proportions from the initial study have significantly changed.
• At 1% significance level, there is sufficient sample evidence to support the claim that proportions from the initial study have significantly changed.