Question

Question 14 1 pts A survey claims that 9 out of 10 doctors (ie. 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of doctors was taken. Suppose the test statisticis z --2.23. Can we conclude that the null hypothesis should be rejected at the a) a =0.10, b) a = 0.05, and c) a = 0.01 level? a) no; b) no; c) yes a) no; b) no; c) no a) yes; b) yes; c) yes a) yes; b) yes; c) no

Answer 1

The correct option is (D), i.e., (a) yes, (b) yes, (c) No.

The null and alternative hypothesis are given as :

$H_{0}:p=0.90$ and $H_{a}:p<0.90$

Since we are testing a legt-tailed hypothesis and the value of Z-statistic is given as $Z=-2.23$ , then the p-value is calculated as follows:

$\mathrm{P-value=P(Z<-2.23)=0.01287372\approx \mathbf{0.0129}}$

So the p-value is calculated as ${\color{Blue} P-value=0.0129}$

(a) For

a = 0.10

$\mathrm{Since,\:\:P-value=0.0129<\alpha=0.10}\Rightarrow\mathbf{ {\color{Teal} We\:reject\:null\:hypothesis\:H_{0}}}$

(b) For $\alpha=0.05$

$\mathrm{Since,\:\:P-value=0.0129<\alpha=0.05}\Rightarrow\mathbf{ {\color{Teal} We\:reject\:null\:hypothesis\:H_{0}}}$

(c) For $\alpha=0.01$

$\mathrm{Since,\:\:P-value=0.0129\nless \alpha=0.01}\Rightarrow\mathbf{ {\color{Teal} We\:fail\:to\:reject\:null\:hypothesis\:H_{0}}}$