According to a study in a previous? year, 57.0?% of households nationwide used natural gas for heating during a year.? Recently, a survey of 3500 randomly selected households showed that 58.0?% used natural gas. Use a 0.05 significance level to test the claim that the 57.0?% national rate has changed.
a) Formulate the null and alternative hypotheses. Choose the correct answer below.
H0 : p = 0.57
Ha : p =/0.57 (not equal)
b) Find the test statistic.
z = _______ ?(Round to two decimal places as? needed.)
c) Find the? P-value for the found test statistic.
P - value = __________ ?(Round to four decimal places as? needed.)
d) State the conclusion. Choose the correct answer below.
A. Do not reject H0. There is sufficient evidence to support the claim that the percentage of households using natural gas has changed.
B. Do not reject H0. There is insufficient evidence to support the claim that the percentage of households using natural gas has changed.
C. Reject H0. There is sufficient evidence to support the claim that the percentage of households using natural gas has changed.
D. Reject H0. There is insufficient evidence to support the claim that the percentage of households using natural gas has changed.