om a sociodemographic Risk factors in spousal abuse study it

om a socio-demographic Risk factors in spousal abuse study, it is observed that the distribution of ages in a sample is as follows: Age Number in sample 20-24 103 25-34 216 35-44 171 Total Conduct a chi-square goodness of fit at the 10 % significance level to test whether the sample provides a good match to the known age distribution in the population. The known percentages are 18%, 50%, 32% Ho: ____________ versus Ha: ____________ The expected number in each category is ______, _______, _______ Which group above seems to be underrepresented in the sample?_____________ The chi-squared test statistic is ________________ The critical value from the chi-squared table is _____________ The p-value is ___________ Will you reject Ho? Explain in the context of the problem ___________________________________________________

Solution

om a socio-demographic Risk factors in spousal abuse study, it is observed that the distribution of ages in a sample is as follows: Age Number in sample 20-24 103 25-34 216 35-44 171 Total Conduct a chi-square goodness of fit at the 10 % significance level to test whether the sample provides a good match to the known age distribution in the population. The known percentages are 18%, 50%, 32%

Ho: Age distribution in the population is same as given versus

Ha: Age distribution in the population is not same as given

The expected number in each category is 88.2, 245, 156.8

Which group above seems to be underrepresented in the sample? 25-34 group

The chi-squared test statistic is 7.202

The critical value from the chi-squared table is 4.605

The p-value is 0.0273

Will you reject Ho?

Calculatedp=0.0273 < 0.10, the level of significance

Reject Ho

Explain in the context of the problem

We conclud ethat the sample does not provides a good match to the known age distribution in the population

Goodness of Fit Test

observed

expected

O - E

(O - E)