Question

A humane society claims that less than 35% of U.S. households own a dog. In a random sample of 400 U.S. households, 156 say they own a dog. At the 10% level of significance is there enough evidence to support the society’s claim? Note: Show (a) The hypothesis structure, (b) The p-value and if you accept or reject the claim, (c) The conclusion as a verbal statement.

Answer 1

Solution :

This is the left tailed test .

The null and alternative hypothesis is

H0 : p =0.35

Ha : p <0.35

n = 400

x =156

= x / n = 156 / 400 =0.39

P0 = 0.35

1 - P0 = 1 - 0.35 =0.65

Test statistic = z

= - P0 / [P0 * (1 - P0 ) / n]

=0.39 -0.35 / [(0.35*0.65) / 400 ]

= 1.68

Test statistic = z =  1.68

P(z < 1.68 ) = 0.9535

P-value = 0.9535

= 0.10

0.9535 > 0.10

P-value <

Fail to reject the null hypothesis .

There is insufficient evidence to suggest that