The most recent census data indicated that 70 percent of a city community was Ca
ID: 3133903 • Letter: T
Question
The most recent census data indicated that 70 percent of a city community was Caucasian, 20 percent Black, and 10 percent Hispanic. A random sample of 200 employees of a large firm in this city revealed that 160 were Caucasian, 30 were Black, and 10 were Hispanic. At the 1 percent significance level can we conclude that the distribution of the firm employees does not reflect the general population?
The null hypothesis is
H0: pC = 0.80, pB = 0.15, pH = 0.05
H0: pC = 0.70, pB = 0.20, pH = 0.10
H0: pC 0.70 or pB 0.20 or pH 0.10
H0: pC 0.80 or pB 0.15 or pH 0.05
2.
The expected frequency for the Black category is
40
30
60
50
3.
The value of the test statistic is
10.357
5.432
13.192
8.715
4.
At 1% significance level, the null hypothesis can be rejected if the value of the test statistic is
11.345
< 11.345
9.210
6.635
5.
The most recent recent census data indicated that 70 percent of a city community was Caucasian, 20 percent Black, and 10 percent Hispanic. A random sample of 200 employees of a large firm in this city revealed that 160 were Caucasian, 30 were Black, and 10 were Hispanic. At the 1 percent significance level can we conclude that the distribution of the firm employees does not reflect the general population?
At 1% significance level, one can conclude that
The distribution of the firm employees reflects the city community
The firm can be accused of engaging in prejudicial hiring practices.
The firm cannot be accused of engaging in prejudicial hiring practices
There is insufficient information to make any conclusion
H0: pC = 0.80, pB = 0.15, pH = 0.05
H0: pC = 0.70, pB = 0.20, pH = 0.10
H0: pC 0.70 or pB 0.20 or pH 0.10
H0: pC 0.80 or pB 0.15 or pH 0.05
2.
The expected frequency for the Black category is
40
30
60
50
3.
The value of the test statistic is
10.357
5.432
13.192
8.715
4.
At 1% significance level, the null hypothesis can be rejected if the value of the test statistic is
11.345
< 11.345
9.210
6.635
5.
The most recent recent census data indicated that 70 percent of a city community was Caucasian, 20 percent Black, and 10 percent Hispanic. A random sample of 200 employees of a large firm in this city revealed that 160 were Caucasian, 30 were Black, and 10 were Hispanic. At the 1 percent significance level can we conclude that the distribution of the firm employees does not reflect the general population?
At 1% significance level, one can conclude that
The distribution of the firm employees reflects the city community
The firm can be accused of engaging in prejudicial hiring practices.
The firm cannot be accused of engaging in prejudicial hiring practices
There is insufficient information to make any conclusion
Explanation / Answer
1.
As given,
OPTION B: H0: pC = 0.70, pB = 0.20, pH = 0.10 [ANSWER]
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2.
20% are black, so
E(B) = 0.20*200 = 40 [ANSWER, A]
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3.
Doing an observed/expected value table,
O E (O - E)^2/E
160 140 2.857142857
30 40 2.5
10 20 5
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 10.35714286 [ANSWER, A]
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4.
As df = a - 1,
a = 3
df = a - 1 = 2
Then, the critical chi^2 value is
significance level = 0.01
chi^2(crit) = 9.210340372 [ANSWER, C]
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5.
As chi^2 > 9.210, we reject Ho. Hence,
OPTION B: The firm can be accused of engaging in prejudicial hiring practices. [ANSWER]