Question

according to a study in a previous year, 59% of households nationwide use natural gas for heating during a year. Recently a survey of 3700 randomly selected household showed that 60% use natural gas use a .05 significance level to test the claim that 59% national rate has changed.

Find the test statistic and the P-value before stating your conclusion

Answer 1

Solution:

Claim is "59% national rate has changed."

So the null and alternative hypothesis are

H₀ : p = 0.59 vs H₁ : p   0.59

n = 3700

Let be the sample proportion.

= 60% = 0.60

1)

The test statistic z is

z =  

=  (0.60 - 0.59)/[0.59*(1 - 0.59)/3700]

= 1.24

Test statistic z = 1.24

2)

There is sign in the alternative hypothesis .

So , TWO tailed test

So ,

p value = P(Z < -z) + P(Z > +z) = P(Z < -1.24) + P(Z > +1.24) = 0.1075 + 0.1075 = 0.2150

p value = 0.2150