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 1006 Chevrolet owners and found that 488 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) State the null and alternate hypotheses. (Pick one)

H₀: p = 0.47; H₁: p ≠ 0.47

H₀: p > 0.47; H₁: p = 0.47    

H₀: p = 0.47; H₁: p > 0.47

H₀: p = 0.47; H₁: p < 0.47

(b) What sampling distribution will you use? (Pick one)

The standard normal, 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.

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

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

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

(e) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? (Pick one)

At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.    

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

Answer 1

a) The null and alternative hypothesis is

H0: p = 0.47; H1: p > 0.47

b) n = 1006 and p = 0.47

np = 1006*0.47 =472.82>5

nq = 1006*0.53 =533.18 >5

Hence , the sampling distribution is The standard normal, since np > 5 and nq > 5

c) The sample proportion is

Under H0, the test statistic is

d) The P-Value is 0.1711

Significance Level

e) Since p value is greater than significance level . Fail to Reject H0.

At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.