Question

Are you an impulse​ shopper? A survey of 800 grocery shoppers indicated that 48 ​% of males and 40 ​% of females make an impulse purchase every time they shop. Assume that the survey consisted of 400 males and 400 females.

a. At the 0.1 level of​ significance, is there evidence of a difference in the proportion of males and females who make an impulse purchase every time they​ shop?

b. Find the​ p-value and interpret its meaning.

Answer 1

a)

p1cap = X1/N1 = 192/400 = 0.48
p1cap = X2/N2 = 160/400 = 0.4
pcap = (X1 + X2)/(N1 + N2) = (192+160)/(400+400) = 0.44

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: p1 = p2
Alternate Hypothesis, Ha: p1 ≠ p2

Test statistic
z = (p1cap - p2cap)/sqrt(pcap * (1-pcap) * (1/N1 + 1/N2))
z = (0.48-0.4)/sqrt(0.44*(1-0.44)*(1/400 + 1/400))
z = 2.28

Rejection Region
This is two tailed test, for α = 0.1
Critical value of z are -1.64 and 1.64.
Hence reject H0 if z < -1.64 or z > 1.64

reject the null hypothesis.

b)

P-value Approach
P-value = 0.0226
As P-value < 0.1, reject the null hypothesis.