Answer: a) [tex]H_0: p=0.1\\H_a:p>0.1[/tex]
b) 2.166666
c) 1.2816
d) Conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point.
Step-by-step explanation:
Let p be the population proportion.
As per given , Company B can reject the shipment if they can conclude that the proportion of defective items in the shipment is larger than 0.1.
Thus, the appropriate hypotheses :
a) [tex]H_0: p=0.1\\H_a:p>0.1[/tex], since alternative hypothesis is right-tailed , so the test is a right-tailed test.
Also , n=400
sample proportion of defective : [tex]\hat{p}=\dfrac{53}{400}=0.1325[/tex]
b) Test statistic : [tex]z=\dfrac{\hat{p}-p}{\sqrt{\dfrac{p(1-p)}{n}}}[/tex]
[tex]z=\dfrac{0.1325-0.1}{\sqrt{\dfrac{0.1(1-0.1)}{400}}}\approx2.1666666[/tex]
c) Using , z-value table ,
Critical value for 0.1 level of significance.:[tex]z_{0.1}=1.2816[/tex]
Since, the test statistic value(2.166666) is greater than the critical value (1.2816) so we reject the null hypothesis.
d) Conclusion: We conclude that the defective proportion in the shipment is greater than 0.1 because the test statistic is larger than the critical point.
