Question

According to a Pew Research Center nationwide telephone survey of American adults, 75% of adults said that college education has become too expensive for most people, and they cannot afford it. One wants to find the probability that in a random sample of 1400 adult Americans, more than 76.5% of the adults in this sample will hold this opinion. Find the z score only.

Answer 1

The z score is 1.324.

Explanation:

We are given that according to a Pew Research Center nationwide telephone survey of American adults, 75% of adults said that college education has become too expensive for most people, and they cannot afford it.

Also, a random sample of 1400 adult Americans is taken.

Let p = % of adults who said that college education has become too expensive according to a Pew Research Center nationwide telephone survey.

Now, the z score probability distribution for sample proportion is given by;

Z =
`\frac{\hat p -p}{\sqrt{(\hat p(1-\hat p))/(n) } }` ~ N(0,1)

where,
`\hat p` = % of the adults in the sample of 1400 adult Americans who hold this opinion = 76.5%

n = sample of Americans = 1400

Now, probability that in a random sample of 1400 adult Americans, more than 76.5% of the adults will hold this opinion is given by = P(
`\hat p` > 76.5%)

The z-score is =
`\frac{0.765-0.75}{\sqrt{(0.765(1-0.765))/(1400) } }`

= 1.324

Therefore, the z score is 1.324.