Question

4. In this question, you will examine the relationship between survival and gender. (a) Obtain the contingency table of survival by gender. Make sure that Row percent, Column percent, and Chi-Square options are checked in each contingency table dialog box. Paste the table into your report. Using a = 0.01, test that there was no relationship between survival and gender. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion. (b) Using a = 0.01, is there evidence that there was a difference in the survival rate for women and men? Carry out the appropriate two-sample proportion test. State the null and alternative hypotheses. Report the value of the appropriate test statistic, the distribution of the test statistic under the null hypothesis, and the P-value of the test to answer the question. State your conclusion. (c) What is the relationship between the tests in parts (a) and (b)?

Answer 1

1)
Null: Gender and survival are independent
Alternate: they are not independent

TS = 365.8869

this is chi-square distribution

p-value < 0.0001

since p-value < alpha
we reject the null hypothesis

we conclude that there is significant relationship

b)

this 2-sample proportion

Z = (p1^ - p2^)/(sqrt(pbar * (1-pbar)(1/n1+ 1/n2))

where pbar = (X1 + X2)/(n1+ n2 )

c)

2-tailed 2-proportion test has same p-value as chi-square