Question

5. A study of the survival of small businesses chose a random sample from the telephone directory’s Yellow Pages listings. Interviews were completed with 148 businesses; 106 were headed by men and 42 by women. Three years later, 22 of those businesses had failed: 15 headed by men, 7 by women. (Use 3 decimal places)

a. Is there a significant difference between the rate at which businesses headed by men and those headed by women fail? Formulate and test the appropriate hypotheses at the 5% level.

Report the value of the test statistic as well as the P-value and your decision. (10 points)

b. Report also a 95% CI. Write one complete sentence expressing the result. (5 points)

Answer 1

i have rounded off all the answers and the proportions to 3 decimal places.

i am denoting men by group 1 and female by group 2.

given data and some calculations are :-

the pooled proportion be:-

hypothesis:-

the test statistic is :-

the p value is :-

[ in any blank cell of excel type =NORMSDIST(-0.385)]

decision:-

p value = 0.700 > 0.05 (alpha)

so, we fail to reject the null hypothesis.There is not sufficient evidence to claim that there a significant difference between the rate at which businesses headed by men and those headed by women fail at 0.05 level of significance.

b).z critical value for 95% confidence level, both tailed test be:-

the 95% confidence interval for the difference between the rate at which businesses headed by men and those headed by women fail is :-

interpretation:-

we are 95% confident that the true difference between the rate (proportion) at which businesses headed by men and those headed by women fail will lie within the interval.

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