Answer:
The approximate probability is 0.1921.
Step-by-step explanation:
The <em>p</em>-value is 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.
The hypothesis to test whether the proportion of consumers that plan to buy a new TV screen within the next year is 0.22, is defined as:
<em>H₀</em>: The proportion of consumers that plan to buy a new TV screen within the next year is 0.22, i.e. <em>p</em> = 0.22.
<em>Hₐ</em>: The proportion of consumers that plan to buy a new TV screen within the next year is 0.22, i.e. <em>p</em> > 0.22.
The information provided is:
<em>n</em> = 230
<em>X</em> = 56
Compute the value of sample proportion as follows:
Compute the test statistic as follows:
The test statistic value is, 0.87.
Compute the <em>p</em>-value as follows:
*Use a <em>z</em>-table for the probability.
The <em>p-</em>value of the test is 0.1921.
Thus, the approximate probability of obtaining a sample proportion equal to or larger than the one obtained here is 0.1921.