Question

Conduct the following test at the a=0.10 level of significance by determining

​ (a) the null and alternative​ hypotheses,

(b) the test​ statistic

(c) the critical value. Assume that the samples were obtained independently using simple random sampling.

Test whether  p1≠p2. Sample data are x 1 = 28, n 1= 254, x 2 = 36, and n 2= 301

Answer 1

Solution:

a)

The  null and alternative​ hypotheses are

H₀ :   = vs H_a :     

b)

₁ = x1 / n1 = 28/254 = 0.1102

₂ = x2 / n2 = 36/301 = 0.1196

Let be the pooled proportion.

= (x1 +x2)/(n1 + n2) = (28+36)/(254+301) = 0.1153

1 - = 1 - 0.1153 = 0.8847

The test statistic z is

z =  

   = (0.1102 - 0.1196)/[0.1153*0.8847*((1/254)+(1/301))]

= -0.345

Test statistic z = -0.345

c)

= 0.10

/2 = 0.05

sign in Ha.

So , the test is TWO tailed.

So , critical values are

Critical values are -1.645 , 1.645

d)

Decision:

Fail to reject H₀

(Because z = -0.345 is not in the rejection region.)

e)

Conclusion:

There is not sufficient evidence to support the claim that