For a random sample of 20 children, 18 attended preschool and 2 did not attend preschool. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \pi=75 \
H_{1}: \pi \neq .75
\end{array}$

Question

For a random sample of 20 children, 18 attended preschool and 2 did not attend preschool. Test the following hypotheses at the .05 level of significance:

$\begin{array}{l}
H_{0}: \pi=75 \
H_{1}: \pi \neq .75
\end{array}$

Quizplus · Accepted Answer

The Answer is

z=\frac{p-\pi_{0}}{\sqrt{\frac{\pi_{0}\left(1-\pi_{0}\right)}{n}}}=\frac{.90-.75}{\sqrt{\frac{75(1-.75)}{20}}}=\frac{.15}{\sqrt{\frac{.75(.25)}{20}}}=\frac{.15}{.0968}=1.55

Using the z table, we find critical values of +/-1.96 (split alpha in ½ given a two-tailed test thus 1 - .025 or .975; find P(z) = .975 in the table; this corresponds to z of 1.96). Since z of 1.55 (test statistic value) is less than our critical value (+1.96), we fail to reject the null hypothesis.

For a Random Sample of 20 Children, 18 Attended Preschool H0:π=75H1:π≠.75\begin{array}{l}H_{0}: \pi=75 \\H_{1}: \pi \neq .75\end{array}H0​:π=75H1​:π=.75​

For a Random Sample of 20 Children, 18 Attended Preschool $\begin{array}{l}H_{0}: \pi=75 \\H_{1}: \pi \neq .75\end{array}$