Question

Answer the following questions keeping a minimum of 4 decimal places for intermediate calculations and round final answers to 2 decimal places.   You must show all your work to receive any marks

1. According to the National Automobile Dealers Association, the mean price for used cars is $10, 192. A manager of a Kansas City used car dealership reviewed a sample of 50 recent used car sales at the dealership in an attempt to determine whether there is evidence that the population mean price is now less than the national average. The sample data revealed an average price of $9,750 and a sample standard deviation of $1400

1. Set up the Hypothesis ( 2 points)

2. Identify which distribution (e.g., z, t, F, binomial, poisson) you would use to analyze the data and state why you choose this distribution (2 points)

3. Calculate the value of test statistic (observed value) ( 4 points)

4. With a critical value of -1.67, what is the statistical decision of this test (i.e., Reject the null or Fail to reject the null? ( 4 points)

Answer 1

Solution :-

Given :-

Mean ( u ) = 10192 $

Sample Mean ( X ) = 9750 $

Sample St. Deviation (s) = 1400 $

Sample Size (n) = 50

Significance Level (α) = 0.05

a)

Null and Alternative Hypotheses :-

Ho: μ = 10192

Ha: μ < 10192

Left tailed test

b)

use t - dirtibution since Sample standard deviation is given ( Sigma unknown )

c)

Test Statistics

d)

Rejection Region

t critical = -1.67 ( Given )

Since it is observed that t = -2.23 < t critical = -1.67 , it is then concluded that the null hypothesis is rejected.

Reject H0