Question

According to a study in a previous? year, 61.0?% of households nationwide used natural gas for heating during a year.? Recently, a survey of 4,600 randomly selected households showed that 62.0?% used natural gas. Use a 0.05 significance level to test the claim that the 61.0?% national rate has changed.

Answer 1

H0: p = 0.61

Ha: p 0.61 (Two tailed)

Test statistics

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

= 0.62 - 0.61 / sqrt( 0.61 * 0.39 / 4600)

= 1.3905

This is test statistics value.

Critical values at 0.05 level are -1.96 , 1.96

Since test statistics value is between critical values -1.96 and 1.96, we do not have sufficient

evidence to reject H0.

We conclude at 0.05 level that we fail to support the claim that the 61% national rate has changed.

Two tailed p-value is calculated as

p-value = 2 * P( Z > 1.3905)

= 2 * 0.0822

= 0.1644

p-value = 0.1644