Question

*USA Today* reported that about 47% of the general
consumer population in the United States is loyal to the automobile
manufacturer of their choice. Suppose Chevrolet did a study of a
random sample of 1007 Chevrolet owners and found that 485 said they
would buy another Chevrolet. Does this indicate that the population
proportion of consumers loyal to Chevrolet is more than 47%? Use
*α* = 0.01.

What is the value of the sample test statistic? (Round your answer
to two decimal places.)

(c) Find the *P*-value of the test statistic. (Round your
answer to four decimal places.)

Answer #1

Solution :

This is the two tailed test .

The null and alternative hypothesis is

H_{0} : p = 0.47

H_{a} : p > 0.47

= x / n = 485 / 1007 = 0.4816

P_{0} = 0.47

1 - P_{0} = 0.53

Test statistic = z

=
- P_{0} / [P_{0
*} (1 - P_{0} ) / n]

= 0.4816 - 0.47 / [(0.47 * 0.53) / 1007]

= 0.74

P(z > 0.74) = 1 - P(z < 0.74) = 0.2297

P-value = 0.2297

USA Today reported that about 47% of the general
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