Question

A goodness of fit test will be conducted for the following hypotheses. This type of test is always an upper tail test. The p-value approach will be used, meaning that the given level of significance, α = 0.01, will be compared to the area under the curve to the right of the calculated test statistic.

H0 : pA = 0.40, pB = 0.40, and pC = 0.20
Ha : The population proportions are not pA = 0.40, pB = 0.40, and pC = 0.20.
The goal of the hypothesis test is to determine if the observed proportions are significantly different from the given proportions. A sample size of 200 yielded 20 in category A, 100 in category B, and 80 in category C. Assuming the hypothesized proportions are true, then the expected frequencies in each category will be the product of the hypothesized proportions and the sample size.
expected frequency = category proportion(sample size)
The proportion for category A is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, eA.
expected frequency = category proportion(sample size)
eA = ( _____ ) (200)
The proportion for category B is assumed to be 0.40. Use the sample size of 200 to find the expected frequency for this category, eB
expected frequency = category proportion(sample size)
eB = ( ______ ) (200)
The proportion for category C is assumed to be 0.20. Use the sample size of 200 to find the expected frequency for this category, ec expected frequency = category proportion(sample size)
eC = ( ______ )(200)

Answer 1

1. 80

2. 80

3. 40

Explanation:

The question requires us to Use the sample size of 200 to find the expected frequency for categories A, B and C

1. (Category proportion)(sample size)

eA = 0.40x200

= 80

2. (Category proportion)(sample size)

eB = 0.40x200

= 80

3. (Category proportion)(sample size)

eC = 0.20 x 200

= 40

The answers are 80, 80 and 40 respectively.