Answer:
The correct option is (B).
Step-by-step explanation:
The p-value is well-defined as per the probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic.
In this case, we need to test the claim that the majority of voters oppose a proposed school tax.
The hypothesis can be defined as follows:
<em>H</em>₀: The proportion of voters opposing a proposed school tax is not a majority, i.e. <em>p</em> ≤ 0.50.
<em>Hₐ</em>: The proportion of voters opposing a proposed school tax is a majority, i.e. <em>p</em> > 0.50.
It is provided that the test statistic value and <em>p</em>-value are:
<em>z</em> = 1.23
<em>p</em>-value = 0.1093
The probability, [under the null-hypothesis (H₀)], of attaining a result equivalent to or more extreme than what was the truly observed value of the test statistic is 0.1093.
The significance level of the test is:
<em>α</em> = 0.05
The <em>p</em>-value of the test is larger than the significance level of the test.
<em>p</em>-value = 0.1093 > <em>α</em> = 0.05
The null hypothesis will not be rejected.
Concluding that there is not enough evidence to support the claim.
Thus, the correct option is:
"If the null hypothesis is true, then the probability of getting a test statistic that is as or more extreme than the calculated test statistic of 1.23 is 0.1093. This result is not surprising (or considered unusual) and could easily happen by chance"
