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Answer:
(a) The <em>p</em>-value of the test statistic is 0.147.
(b) The <em>p</em>-value of the test statistic is 0.294.
(c) The <em>p</em>-value of the test statistic is 0.8531.
(d) None of the <em>p</em>-values give strong evidence against the null hypothesis.
Step-by-step explanation:
The <em>p</em>-value is well defined as the probability,[under the null hypothesis (H₀)], of attaining a result equivalent to or greater than what was the truly observed value of the test statistic.
We reject a hypothesis if the p-value of a statistic is lower than the level of significance <em>α</em>.
The null hypothesis for the test of population proportion is defined as:
<em>H₀</em>: <em>p</em> = 0.50
The value of <em>z</em>-test statistic is,
<em>z</em> = 1.05
(a)
The alternate hypothesis is defined as:
<em>Hₐ</em>: <em>p</em> > 0.50
Compute the <em>p</em>-value of the test statistic as follows:
*Use a <em>z</em>-table for the probability value.
Thus, the <em>p</em>-value of the test statistic is 0.147.
(b)
The alternate hypothesis is defined as:
<em>Hₐ</em>: <em>p</em> ≠ 0.50
Compute the <em>p</em>-value of the test statistic as follows:
*Use a <em>z</em>-table for the probability value.
Thus, the <em>p</em>-value of the test statistic is 0.294.
(c)
The alternate hypothesis is defined as:
<em>Hₐ</em>: <em>p</em> < 0.50
Compute the <em>p</em>-value of the test statistic as follows:
*Use a <em>z</em>-table for the probability value.
Thus, the <em>p</em>-value of the test statistic is 0.8531.
(d)
The decision rule of the test is:
If the <em>p</em>-value of the test is less than the significance level <em>α</em>, then the null hypothesis is rejected at <em>α</em>% level of significance.
And if the <em>p</em>-value of the test is more than the significance level <em>α</em>, then the null hypothesis is failed to be rejected.
The most commonly used level of significance are:
<em>α</em> = 0.01, 0.05 and 0.10
The <em>p</em>-value for all the three alternate hypothesis are:
<em>p-</em>values = 0.147, 0.294 and 0.8531.
All the <em>p</em>-values are quite large compared to the <em>α</em> values.
Thus, none of the <em>p</em>-values give strong evidence against the null hypothesis.
The null hypothesis was failed to be rejected.