Question

A mortgage broker believes that the typical family that rents their home owns fewer than 2 cars on average. A random sample of 26 families that rent their home owned an average of 1.29 cars with a standard deviation of 0.97 cars. At the 0.05 level of significance, test the claim that the average number of cars owned by families that rent their home is not 2. (Based on the results of the Census Bureau American Housing Brief.)

a. What is the null hypothesis stated in English or by symbols? b. What is the alternative hypothesis stated in English or by symbols? c. What is the test statistic or the confidence interval? (Show all justifications.) d. What is your conclusion in terms a sixth grade student would understand?

Answer 1

a)

Null Hypothesis H0: = 2

b)

Altenative Hypothesis Ha:   < 2

c)

Sample mean, = 1.29

Sample standard deviation s = 0.97

Since we do not know the true population standard deviation we will conduct one sample t test.

Standard error of mean, SE = s / = 0.97 / = 0.1902327

Test statistic, t = ( - ) / SE =  (1.29 - 2) / 0.1902327 = -3.73

d.

Degree of freedom = n-1 = 26-1 = 25

p-value = p(t < -3.73 , df = 25) =  0.0005

Since, p-value is greater than 0.05 significance level, we reject null hypothesis H0.

We conclude that there is sufficient evidence from the sample data that typical family that rents their home owns less than 2 cars on average.