z pvalueSolutionHere we have to test the hypothesis that H0

z=______

p-value=____

Here we have to test the hypothesis that,

H0 : p = 0.48 Vs H1 : p 0.48

where p is the population proportion of households with no children

given that ,phat = 0.43

variance of p^ = [ p*(1-p) / n ]

n = number of respondants in a christmas tree market survey = 420

variance = ( 0.48*0.52 ) / 420 = 0.000594

sd = sqrt(0.000594) = 0.024378

The test statistic for testing proportion is,

Z = (p^ - p) / sd

= (0.43 - 0.48) / 0.024378

Z = -2.05

P( |z| > 2.05) = 0.0202

alpha = 0.1

P-value command in EXCEL,

=NORMSDIST(z)

where z is the test statistic value.

P-value < alpha

Reject H0 at 0.1 significance level.

We conclude that the proportion of households with no children differs from 48%.