Question

A polling agency claims that 60% of adult in our country think that the Federal Government bailout of troubled bank was very bad for the country. In random sample of 278 U.S. adults, 157 said that indeed the bailout was very bad for the country. At a 0.01 level of significance, is there enough is there enough evidence to support the banks claim?

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H₀ : p = 0.60

H_a : p 0.60

= x / n = 157 / 278 = 0.5647

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.5647 - 0.60 / [(0.60 9* 0.40) / 278]

= -1.2

P(z < -1.2) = 0.1151

P-value = 2 * 0.1151 = 0.2302

= 0.01

P-value >

Fail to reject the null hypothesis .

There is not sufficient evidence to suggest that the banks claim .