Question

A 0.05 significance level is used for a hypothesis test of the claim that when parents use a particular method of gender​ selection, the proportion of baby girls is less than 0.5. Assume that sample data consists of 78 girls in 169 ​births, so the sample statistic of six thirteenths results in a z score that is 1 standard deviation below 0. Complete parts​ (a) through​ (h) below. Identify the null hypothesis and the alternative hypothesis. What is the value of a? What is the sampling distribution of the sample​ statistic? Is the test​ two-tailed, left-tailed, or​ right-tailed? What is the value of the test​ statistic? What is the​ P-value? What are the critical​ value(s)? What is the area of the critical​ region?

Answer 1

a) Null and alternative hypothesis:

Ho: p= 0.5

H1: p< 0.5

b) Significance level, = 0.05

c) Sampling distribution:

n = 169, x = 78

Sample proportion, = 78/169 = 0.4615

d) It is a left tailed test.

e) Test statistic:

f) P-value = NORM.S.DIST(-1, 1) = 0.1587

g) Critical vale:

At = 0.05, left tailed critical value, z_c = NORM.S.INV(0.05) = -1.645

h) Area of critical region:

R= {z :z<-1.64}