Significance tests A test of$H_0:p=0.5$versus Ha : p >0.5 has test statistic z=2.19.

(a) What conclusion would you draw at the 5 % significance level? At the 1 % level?

(b) If the alternative hypothesis were $H_0:p\ne 0.5$what conclusion would you draw at the 5% significance level? At the 1 % level?

A p-value is a factual estimation used to approve a theory against noticed information. A p-esteem estimates the likelihood of getting the noticed outcomes, it is consistent with expectations that the invalid speculation. The lower the p-esteem, the more prominent the factual meaning of the noticed distinction.

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.5\\ H_a:p>0.5\end{array}$

Calculating the p-value by using,

$=P(Z>|z\left|\right)$

$=P(t>|2.19\left|\right)=0.0143$

The null hypothesis is rejected at$5\%$ significance level and not rejected at$1\%$ significance level as the p-value is less than$5\%$and greater than$1\%$.

Calculating the null and alternative hypotheses,

$\begin{array}{r}{H}_0:p=0.5\\ H_a:p\ne 0.5\end{array}$

The p-value is calculated as,

$=2\times P(Z>|Z\left|\right)$

$=2\times 0.014=0.028$

The null hypothesis is not rejected in both cases.