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 120 people whether or not they supported the proposed upgrade project.

Data:

yes
no
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
yes
no
yes
yes
yes
no
yes
no
yes
no
yes
yes
yes
yes
no
yes
no
yes
no
yes
no
yes
no
yes
yes
no
yes
yes
yes
yes
no
yes
yes
yes
no
no
no
yes
yes
no
no
yes
no
yes
yes
no
yes
no
yes
no
yes
yes
yes
yes
yes
no
yes
yes
yes
yes
yes
no
yes
yes
yes
no
no
no
no
yes
yes
no
yes
yes
no
yes
no
yes
yes
yes
no
no
yes
no
yes
yes
yes
yes
yes
yes
no
no
yes
yes
yes
no
yes
yes
yes
yes
yes
yes
no
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: _______

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 (rejected or not rejected)

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

Answer 1

a) Here we need to see that whether the support is more than 0.6.

H₀: p < 0.6

H_a: p > 0.6

Therefore, B) is the correct option.

b) The formula to calculate the test statistic is:

p_o = 0.60

p = 0.692 (The proportion of people saying "Yes" from the sample)

n = 120

The test statistic, z = 2.06

Z-critical value at 0.05 significance level, right-tailed = 1.65

As z > critical value of z, hence null hypothesis can be rejected.

c)Therefore, at a significance level of 0.05, the null hypothesis is rejected.

That is, you can state that there is significant evidence to conclude that the population proportion of people who support the proposed upgrade project is greater than 0.6.