Let p denotes the population proportion.
By considering the given information, we have
Null hypothesis : [tex]H_0 : p\leq0.35[/tex]
Alternative hypothesis : [tex]H_1 : p>0.35[/tex], since alternative hypothesis is right tailed so the test is a right tailed test.
Given : n= 1600 ; [tex]\hat{p}=0.38[/tex]
Test statistics for proportion :-
[tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]=\dfrac{0.38-0.35}{\sqrt{\dfrac{0.35(1-0.35)}{1600}}}=2.51588360813\approx2.52[/tex]
P-value for right tailed test = [tex]P(z>2.52)=0.0058677\approx0.006[/tex]
Conclusion : Since the p-value (0.006) is less than significance level (0.02) that means we reject the null hypothesis.
Thus , we conclude that we have sufficient evidence at the 0.02 level to support the company's claim.
