Question

State your conclusion to the hypothesis test. The mayor of a certain city is tasked with cutting over 5 million dollars out of next year’s budget and is considering cuts to spending on public transportation. The mayor decides to conduct a hypothesis test and will only cut spending on public transportation if fewer than 15% of residents use the service. In a random sample of 300 residents, 36 reported that they did use public transportation. Perform the appropriate hypothesis test at a 1% significance level.

a) Reject the null hypothesis. There is sufficient evidence to conclude that fewer than 15% of residents use public transportation.

b) Reject the null hypothesis. There is sufficient evidence to conclude that more than 15% of residents use public transportation.

c) Do not reject the null hypothesis. There is insufficient evidence to conclude that more than 15% of residents use public transportation.

d) Do not reject the null hypothesis. There is insufficient evidence to conclude that fewer than 15% of residents use public transportation.

Answer 1

H0: p 0.15

Ha: p < 0.15

Sample proportion = 36 / 300 = 0.12

Test statistics

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

= ( 0.12 - 0.15) / sqrt ( 0.15 * ( 1 - 0.15) / 300)

= -1.46

p-value = P(Z < z)

= P(Z < -1.46)

= 0.0721

Since p-value > 0.01 level, do not reject H0.

Do not reject the null hypothesis. There is insufficient evidence to conclude that fewer than 15% of

residents use public transportation.