Answer:
The statement that "the margin of error was given as [tex]\pm5[/tex] percentage points" means that the population proportion is estimated to be with a certain level of confidence, within the interval [tex]\hat{p} \pm 0.05[/tex] ; where [tex]\hat{p}[tex] is the sample's proportion.
The correct answer is C. The statement indicates that the interval [tex]0.14\pm0.05[/tex] is likely to contain the true population percentage of people that prefer chocolate pie.
Step-by-step explanation:
The margin of error for proportions is given by the following formula:
[tex]z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}[/tex]
Where:
[tex]z_{\alpha /2}[/tex] is the critical value that corresponds to the confidence level; the confidence level being [tex]1-\alpha[/tex],
[tex]\hat{p}[/tex] is the sample's proportion of successes,
[tex]n[/tex] is the size of the sample.
In this exercise we have that [tex]\hat{p}=0.14[/tex] and that the margin of error is 0.05.
Therefore if we replace in the formula to calculate the confidence interval we get:
[tex]\hat{p}\pm 0.05=0.14\pm0.05=(0.09, 0.19)[/tex]
Which means that the true population proportion is estimated to be, with a certain confidence level, within the interval (0.09, 0.19).
