Students are asked to rate their preference for one of four video games. The fol

Question

Students are asked to rate their preference for one of four video games. The following table lists the observed preferences in a sample of 80 students. State whether to retain or reject the null hypothesis for a chi-square goodness-of-fit test given the following expected frequencies. (Assume alpha equal to 0.05.)

(a) expected frequencies: 25%, 25%, 25%, 25%, respectively

Retain the null hypothesis. Reject the null hypothesis.    

(b) expected frequencies: 70%, 10%, 10%, 10%, respectively

Retain the null hypothesis. Reject the null hypothesis.    

Video Games McStats Tic-Tac
Stats Silly
Stats Super
Stats Frequency
observed 20 20 20 20

Explanation / Answer

a) H0: the observed frequencies are equally proportion

H1:  the observed frequencies are not equally proportion

From the given data

Num Categories: 4
Degrees of freedom: 3

Test Statistic, X^2: 0.0000
Critical X^2: 7.814736
P-Value: 1.0000

Here P-value > alpha 0.05, so we accept H0

Thus we conclude that the observed frequencies are equally proportion

Correct answer: Retain the null hypothesis

b)

H0: the observed frequencies are follows given proportion

H1:  the observed frequencies are not follows given proportion

From the given data

Num Categories: 4
Degrees of freedom: 3

Test Statistic, X^2: 77.1429
Critical X^2: 7.814736
P-Value: 0.0000

Here P-value < alpha 0.05, so we reject H0

Thus we conclude that  the observed frequencies are not follows given proportion

Correct answer: Reject the null hypothesis

Observed Expected Freq (Oi) Freq Ei (Oi-Ei)^2 /Ei 20 20 0 20 20 0 20 20 0 20 20 0 Total: 80 0

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---