State the null and alternative hypotheses, conduct a chi-square goodness-of-fit

Question

State the null and alternative hypotheses, conduct a chi-square goodness-of-fit test, find the p-value and state your decision (retain the null hypothesis or reject the null and accept the alternative). Let alpha be 0.05.

Test whether the observed (sample) of 400 catalog orders “fits” the regional distribution of the US population. Fill in the Expected orders column and conduct the test.

Share of US population Region Observed cat. Orders Expected orders 0.21 NE 68 84 0.24 MW 104 0.35 South 155 0.2 West 73 TOTAL 400

Explanation / Answer

H0: There is no relation between region and catalog orders

H1: There is a relation between region and catalog orders

alpha:5%

Test statistic:

Epected frequency =mean=100

Chi square=47.94

P value=0.000000<0.05, we reject the H0. Hence claim is significant

Hence there is a relationship between region and catalog orders

Oi ei (oi-ei)^2/ei 68 100 10.24 104 100 0.16 155 100 30.25 73 100 7.29

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