Question

A random sample of 18 adults, chosen from the 1500 adults in the town, took a survey asking their opinion on a recent property tax change. 25% of those who responded said they were in favor of the change. The company running the survey wants to construct a confidence interval estimating the proportion of all adults in the town who support the change. Which of the conditions for inference have been satisfied?
I. Random condition

II. Normal condition

III. 10% condition

A) I

B) II

C) I and III

D) II and III

E) I, II, and III

Answer 1

Answer:

C) I & III

Step-by-step explanation:

Given:

Sample size, n = 18

Sample proportion = 25% = 0.25

Here, a random sample of 18 adults were chosen from the 1500 adults in town. This shows that the random condition was satisfied because the sample was drawn randomly from the general population of adults in the town.

For the normal condition to be satisfied, np should be greater than 10, ie np > 10.

In this case, np = 18 * 0.25 = 4.5

Since np is less than 10, the normal condition was not satisfied.

For the 10% condition to be satisfied, sample size should not be more than 10% of the general population.

Here, the sample size is 18 and the population is 1500. Therefore,

$\frac{18}{1500} * 100 = 1.2$

Since the sample size is 1.2% of the population which is less than 10%, the 10% condition was satisfied.

The correct option is C, because only I & III were satisfied.