Question

According to the Energy Administration, 53 of every 100 households, nationwide used natural gas for heating in 2007. A recent survey of 3,600 randomly selected household in London, Ontario, showed that 1,980 of them used natural gas. Use a 0.01 significance level to test the claim that the rate of natural gas use in London greater than the national rate.

a) z = - 2.40 with a p value of .0082 .0082 < .01 Therefore there is sufficient evidence to support the alternative hypothesis that London Residents use natural gas for heating than the national rate.

b) z = 2.40 with a p value of (1-.9918) .0082 < .01 Therefore there is sufficient evidence to support the alternative hypothesis that London Residents use natural gas for heating than the national rate.

c) z = 2.89 with a p value of (1-.9981) .0019 < .01 Therefore there is sufficient evidence to support the alternative hypothesis that London Residents use natural gas for heating than the national rate.

d) z = 2.40 with a p value of .9918 .9918 > .01 Therefore there is NOT sufficient evidence to support the alternative hypothesis that London Residents use natural gas for heating than the national rate.

Answer 1

H0: p = 0.53

Ha: p > 0.53

Sample proportion = 1980 / 3600 = 0.55

Test statistics

z = - p / sqrt( p (1 -p ) / n)

= 0.55 - 0.53 / sqrt( 0.53 * 0.47 / 3600)

= 2.40

This is test statistics value .

p-value = P( Z > z)

= 1 - P (Z < z)

= 1 - P( Z < 2.40)

= 1 - 0.9918

= 0.0082

We conclude that,

z = 2.40 with a p value of (1-.9918) 0082 < 0.01. Therefore there is sufficient evidence to support the

alternative hypothesis that London Residents use natural gas for heating than the national rate.