Answer
a) $373$
b) Between $34.2\%$ and $40.2\%$.
c) Yes
d) The criticism is unfounded.
Work Step by Step
a) The number who said yes is:
$1003\cdot0.372=373$
b) We need to find the margin of error. 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 $0.03=3\%$.
Hence, 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 can see that the value of P is about $0$. Hence, we reject the null hypothesis, so we accept the test hypothesis.
d) The sample size is small, but we see that the criticism that it is too small is unfounded, because the results from part c) show that accepting the test hypothesis is valid.
