Question

The local government is considering implementing a roads and public transport infrastructure upgrade project. Before they commit to this however, they would like to canvas public opinion to gauge community support for such a project. If it they are convinced that more than 60% of the community support the proposed upgrade project, then the government will commission the project.

The following sample was collected by asking a randomly selected group of 110 people whether or not they supported the proposed upgrade project.

yes yes yes no no yes yes yes yes yes yes yes no yes yes yes yes yes yes no yes no yes no no yes yes yes yes no no no yes no no no no no yes yes yes yes no yes yes yes yes yes no yes yes no yes no yes yes yes yes yes no yes yes yes yes yes no yes yes yes yes yes yes no no yes yes yes no yes yes no yes yes yes yes yes yes no no yes yes yes yes no yes yes yes no no yes yes no no no yes no yes yes yes yes

Download the data

Survey results:
yes	yes	yes	no	no	yes	yes	yes	yes	yes
yes	yes	no	yes	yes	yes	yes	yes	yes	no
yes	no	yes	no	no	yes	yes	yes	yes	no
no	no	yes	no	no	no	no	no	yes	yes
yes	yes	no	yes	yes	yes	yes	yes	no	yes
yes	no	yes	no	yes	yes	yes	yes	yes	no
yes	yes	yes	yes	yes	no	yes	yes	yes	yes
yes	yes	no	no	yes	yes	yes	no	yes	yes
no	yes	yes	yes	yes	yes	yes	no	no	yes
yes	yes	yes	no	yes	yes	yes	no	no	yes
yes	no	no	no	yes	no	yes	yes	yes	yes

The level of significance to be used in the test is α = 0.05.

a)From the following options, select the correct null and alternate hypotheses for this test:

A:H₀: p = 0.6, H_a: p < 0.6

B:H₀: p < 0.6, H_a: p > 0.6

C:H₀: p = 0.6, H_a: p > 0.6

D:H₀: p = 0.6, H_a: p ≠ 0.6

The correct null and alternate hypotheses for this test are: A) B) C) D)?

b)Calculate the test statistic (z) for this hypothesis test. Give your answer to 2 decimal places.

z = ?

c)Therefore, at a significance level of 0.05, the null hypothesis is A) rejected B) not rejected.

That is, you can state that there is A) proof B) significant evidence C) not enough evidence to conclude that the A) population proportion B) sample proportion of people who support the proposed upgrade project is A) less than B) greater than C) equal to 0.6.

Answer 1