Table 1 gives the distribution of the number

basura8w081

basura8w081

Answered question

2022-04-03

Table 1 gives the distribution of the number of acceptances of 100 students into 3 departments in College of Commerce and Business Administration. Test at the 5% level of significance that the distribution of acceptances is approximately binomial if the probability of a student's being accepted into college is 0.40.
What is the computed value of chi-square? Blank 1
What is the tabular value of chi-square? Blank 2
Choose a or b Blank 3
a. Accept the null hypothesis because the tabular value of chi-square is larger than the computed value of chi-square.
b. Accept the alternative hypothesis because the tabular value of chi-square is smaller than the computed value of chi-square.
 Number of Acceptances  Number of Students 025134231310

Answer & Explanation

Madilyn Shah

Madilyn Shah

Beginner2022-04-04Added 11 answers

Given,
probability (p) = .4
Observed frequency (O):
 Number of Acceptances  Number of Students 025134231310 Total100
Let x be a random variable, χ(n=3,p=.4)
P(X=x)=nCxpX(1n)nx
Expected frequency (E) calculation :
xP(x)P(x) Expected value (E)=P(x)Total03C0(.40)(1-.4)100-00.2160.216100=21.613C1(.41)(1-.4)100-10.4320.432100=43.223C2(.42)(1-.4)100-20.2880.288100=28.833C3(.43)(1-.4)100-30.0640.064100=6.4
Chi-square test statistic (χ2):
OE(O-E)2(O-E)2/E2521.611.560.5351853443.284.641.9592593128.84.840.168056106.412.962.025000   Chi-square test statistic (χ2)=4.687500
Chi-square test statistic (χ2)=(OE)2E
= 4.6875
degree of freedom (df)= n-1 = 2
α=0.05
The test statistic follows the χ2-distribution with 2 degrees of freedom.
Tabulated value: 5.9915
Since test statistic < Critical value, we fail to reject the null hypothesis.
Accept the null hypothesis because the tabular values of chi-square is larger than the computed value of chi-square.

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