Question

ACDEFGHIJKLMNOLORSTU 25. Consumer data collected from shopper cards show that, nationwide, 97% of U.S. shoppers buy toilet paper. A grocery store manager thinks that more than 97% of shoppers at his store buy toilet paper. He takes a random sample of 500 shoppers and finds that 490 purchased toilet paper. He wants to test Ho:P < 0.97 versus Hyp>0.97. What is the value of the test statistic and the associated p value?

Answer 1

Solution :

This is the right tailed test .

The null and alternative hypothesis is

H0 : p < 0.97

Ha : p > 0.97

n = 500

x =490

$\hat p$ = x / n = 490 / 500 = 0.98

P0 = 0.97

1 - P0 = 1 - 0.97 = 0.03

Test statistic = z

= $\hat p$ - P0 / [ $\sqrt$ P0 * (1 - P0 ) / n]

= 0.98-097/ [ $\sqrt$ (0.97*0.03) / 500]

= 1.30

Test statistic = z = 1.30

P(z >1.30 ) = 1 - P(z < 1.30 ) = 1 - 0.9032

P-value = 0.0968