Question

a) 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 1002 Chevrolet owners and found that 482 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 T value and the P Value?

Wishart and Leach found that about 26.1% of the five-syllable sequences are of the type in which two are short and three are long. Suppose that Greek archaeologists have found an ancient manuscript dating back to Plato's time (about 427 - 347 B.C.). A random sample of 311 five-syllable sequences from the newly discovered manuscript showed that 60 are of the type two short and three long. Do the data indicate that the population proportion of this type of five syllable sequence is different (either way) from the text of Plato's Republic? Use α = 0.01.

What is the T Value and the P Value?

Answer 1

Ho :p = 0.47

H1 :p >0.47

Level of Significance,α = 0.01

Number of Items of Interest,x =482

Sample Size,n = 1002

Sample Proportion , p̂ = x/n = 0.4810

Standard Error , SE = √( p(1-p)/n ) = 0.0158

Z Test Statistic = Z = ( p̂-p)/SE = 0.70

p-Value=0.2419[Excel function =NORMSDIST(-z)

Conclusion:                            p-value>α , do not reject null hypothesis           

there is not enough evidence that population proportion of consumers loyal to Chevrolet is more than 47% at α=0.01