Answer with explanation:
We are given Sample proportion : [tex]\hat{p}=0.58[/tex]
And Population proportion : p=0.62
By considering company's claim, we have
[tex]H_0:p=0.62\\\\H_a:p\neq0.62[/tex]
Since alternative hypothesis is two-tailed , so the test is two-tailed test.
Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
i.e.[tex]z=\dfrac{0.58-0.62}{\sqrt{\dfrac{0.62(1-0.62)}{900}}}\approx-2.47[/tex]
P-value (two-tailed test)=[tex]2P(z>|-2.47|)=2P(z>2.47)[/tex]
[tex]=0.0135113\approx0.013[/tex]
Since, the p-value is greater than the significance level (0.01), so we accept the null hypothesis.
We conclude that we have enough evidence to support company's claim.
