Question

Determine whether a normal sampling distribution can be used for the following sample statistics. If it can be​ used, test the claim about the difference between two population proportions p1and p2 at the level of significance α. Assume that the samples are random and independent.

​Claim: p 1 ≠ p2​,

α=0.01

Sample​ Statistics: x1=40​, n1=69​, x2=42​, n2=59

Determine whether a normal sampling distribution can be used.

1) The samples are random and independent. A normal sampling distribution ______ be used because n1p= ___, n1q= ___, n2p= ___, and n2q = ___.

​(Round to two decimal places as​ needed.)

2) Calculate the critical value ​(Round to two decimal places as​ needed.)

3) Calculate the test statistic ​(Round to two decimal places as​ needed.)

4)Decide whether to reject or fail to reject the null hypothesis and interpret the decision in the context of the original claim.

Answer 1

1)

The samples are random and independent. A normal sampling distribution can be used because n1p= 69 *(40/69) = 40.00 , n1q = 69 *(29/69) = 29.00, n2p= 59 *(42/59) = 42.00 and n2q = 59 *(17/59) = 17.00.

b)

This is two tailed test, for α = 0.01
Critical value of z are -2.58 and 2.58.
Hence reject H0 if z < -2.58 or z > 2.58

c)

p1= 0.5797
p2= 0.7119

pcap = (40 + 42)/(69 + 59) = 0.6406

z = ( 0.5797 - 0.7119)/sqrt(0.6406 *1-0.6406 ) *(1/69 +1/59))
= -1.55

d)

fail to reject the null hypothesis

There is not sufficient evidence to test the claim about the difference between two population proportions p1and p2