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 1009 Chevrolet owners and found that 483 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.(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: p = 0.47; H₁: p ≠ 0.47H₀: p = 0.47; H₁: p > 0.47    H₀: p = 0.47; H₁: p < 0.47H₀: p > 0.47; H₁: p = 0.47

(b) What sampling distribution will you use?

The standard normal, since np < 5 and nq < 5.The Student's t, since np > 5 and nq > 5.    The standard normal, since np > 5 and nq > 5.The Student's t, since np < 5 and nq < 5.

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

A) Claim: To test whether that the population proportion of consumers loyal to Chevrolet is more than 47% or not

Hypothesis :

  

Right tailed test

Let x = number of chevrolet owners who would buy another chevrolet

Given that

Total number of chevrolet owners = n = 1009

Therefore sample proportion is

B) Note that Here

and

Here both n*p and n*q are greater than 5

So, standard normal distribution is approporiate to use.

Test statistics:

we get z= 0.55 .................(Test statistics)

C) pvalue= ...................(For right tailed)

  

...............(Answer)

Decision Rule : We Fail to Reject Ho

Conclusion: There is insufficient evidence to conclude that the population proportion of consumers loyal to Chevrolet is more than 47%