Which of the following $95\%$confidence intervals would lead us to reject H0 : $p=0.30$ in favor of

Ha :p not equal to $0.30$ at the $5\%$ significance level?

$$\begin{gathered} \left(a\right)(0.29,0.38)\left(c\right)(0.27,0.31)\left(e\right)Noneofthese \\ \left(b\right)(0.19,0.27)\left(d\right)(0.24,0.30) \end{gathered}$$

Confidence level $=95\%$

The null and alternative hypotheses are:$$\begin{gathered} H0:p=0.30 \\ {H}_a:p\ne 0.30 \end{gathered}$$

Confidence intervals give information not found in significance tests, such as a range of feasible values for the true population parameter $p$ A two-sided $H0:p=p0$ test at significance level $a$ yields a result similar to a $100(1-a)$ percent confidence interval.

If the confidence interval does not contain $0.30$the null hypothesis is rejected. The confidence interval $(0.19,0.27)$is the only one that does not contain the value of $0.30$Confidence intervals give information not found in significance tests, such as a range of feasible values for the true population parameter $p$A two-sided $H0:p=p0$test at significance level a yields a result similar to a $100(1-a)$percent confidence interval. This would result in the null hypothesis being rejected. As a result, the best solution is (b).