A job candidate at a large job fair can be classified as unacceptable, provisional, or acceptable. B

Bobrovnik61j

Bobrovnik61j

Answered question

2022-03-02

A job candidate at a large job fair can be classified as unacceptable, provisional, or acceptable. Based on past experience, a high-quality candidate is expected to get 80 percent acceptable ratings, 15 percent provisional ratings, and 5 percent unacceptable ratings. A high-quality candidate was evaluated by 100 companies and received 60 acceptable, 25 provisional, and 15 unacceptable ratings. A chi-square goodness-of-fit-test was conducted to investigate whether the evaluation of the candidate is consistent with past experience. What is the value of the chi-square test statistic and number of degrees of freedom for the test?
a. χ2=(155)25+(2515)215+(6080)280 with 2df
b. χ2=(155)25+(2515)215+(6080)280 with 3df
c. χ2=(155)25+(2515)215+(6080)280 with 99df
d. χ2=(515)215+(1525)225+(8060)260 with 2df
e. χ2=(515)215+(1525)225+(8060)260 with 3df

Answer & Explanation

Zernerqcw

Zernerqcw

Beginner2022-03-03Added 11 answers

It is given that the large job fair classified as unacceptable, provisional, or acceptable. A high-quality candidate is expected to get 80% acceptable, 15% provisional and 5% unacceptable ratings based on past experience.
A high-quality candidate was evaluated by 100 companies and received 60 acceptable, 25 provisional and 15 unacceptable ratings.
Formula for Test statistic:
χ2={i=1}n(OiEi)2Ei
here, Oi is observed frequencies and Ei is expected frequencies.
Observed Frequencies:
 Ratings  Acceptable  Provisional  Unacceptable  Total  Observed Frequencies 602515100
Calculations:
Calculate the expected frequencies:
 Ratings  Acceptable  Provisional  Unacceptable  Total  Expected Frequencies 100×0.80=80100×0.15=15100×0.05=5100
Calculate the chi-square test statistic:
χ2=(155)25+(2515)215+(6080)280
=40080+10015+1005
=5+6.667+20
=31.667
Degrees of freedom:
df=(No.of categories)-1
=3-1
=2
Answer:
The chi-square test statistic is χ2=(155)25+(2515)215+(6080)280 with 2df
Therefore, the correct option is A.

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