Answer
a. 373
b. Between 34.2 percent and 40.2 percent.
c. Yes
d. The criticism is unfounded.
Work Step by Step
a. The number who said yes is:
$=1003\times.372 =373$
b. We need to find the margin of error. We know the following equation for the margin of error:
$E=t_{.025}\frac{s}{\sqrt{1003}}$
Where s is the standard deviation.
Using a standard deviation calculator to find s, we find that the error is .03, which is 3 percent.
Thus, the values can range from 3 below the mean (34.2) to 3 above the mean (40.2).
c. Using a ti-84 and a table of z-values, we see that the value of P is about 0. Thus, we reject the null hypothesis, meaning that we accept the test hypothesis.
d. Even though the sample size is small, we see that the criticism that it is too small is unfounded, for the results from part c show that accepting the test hypothesis is valid.
