Question

A news website believes that equal to 52% of its visitors click on advertisements while on the site. A sample of size 39 visitors is taken and it is observed that 16 of them clicked on ads. Perform a hypothesis test to test the null hypothesis that equal to 52% of website visitors click ads against the alternative hypothesis, H₁, that something other than 52% click on ads, with level of significance α = 0.1.

a)	What type of test would be appropriate in this situation? A right-tailed test. A left-tailed test. A two-tailed test None of the above.

b) What is the computed p-value?
For full marks your answer should be accurate to at least three decimal places.

p-value: 0

c)

Based on your p-value and the decision rule you have decided upon, what can we conclude about H0? There is sufficient evidence, at the given significance level, to reject H0. There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0. There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis

Answer 1

Solution:

a) The null and alternative hypotheses are as follows:

H_{​​​​​​0} : P = 0.52 i.e. The population proportion of visitors click on advertisements while on the site is equal to 0.52.

H_{​​​​​​1} : P ≠ 0.52 i.e. The population proportion of visitors click on advertisements while on the site is not equal to 0.52.

Since, we have two tailed alternative, therefore a two-tailed test would be appropriate here.

b) We shall use two-tailed z test for single proportion to test the hypothesis. The test statistic is given as follows:

Where, p is sample proportion, P is population proportion specified under H_{​​​​​​0}, Q = 1 - P and n is sample size.

Sample proportion of visitors click on advertisements while on the site is,

P = 0.52, Q = (1 - 0.52) = 0.48 and n = 39

The value of the test statistic is -1.37125.

The two-tailed p-value for the test statistic is given as follows:

p-value = 2P(Z < -1.37125)

p-value = 0.1703

The computed p-value is 0.1703.

c) We make decision rule as follows:

If p-value is greater than the significance level then we fail to reject H₀ at given significance level.

If p-value is less than the significance level then we reject H₀ at given significance level.

Given that significance level α = 0.1 and we have p-value = 0.1703.

(0.1703 > 0.1)

Since p-value is greater than the significance level of 0.1, therefore we shall be fail to reject the null hypothesis (H_{​​​​​​0}) at 0.1 significance level.

There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H_{​​​​​​0}.

Please rate the answer. Thank you.