The test statistic is: The alternative hypothesis is: The null hypothesis is:?

A car company says that the mean gas mileage for its luxury sedan is 21 mpg. You believe the mean gas mileage is lower than this and find that a random sample of 5 cars has a mean gas mileage of 19 mpg and a sample standard deviation of 4 mpg. Assume the gas mileage of all of the company鈥檚 luxury sedans is normally distributed. At 伪 = 0.10, use a t-test to assert the validity of the company鈥檚 claim.





The test statistic is:


The alternative hypothesis is:


The null hypothesis is:|||ANSWER: Conclusion: H0 is true








SINGLE SAMPLE TEST, ONE-TAILED, 6 - Step Procedure for t Distributions, "one-tailed test"








Step 1: Determine the hypothesis to be tested.


Lower-Tail


H0: 渭 鈮?渭0 H1: 渭 %26lt; 渭0


or


Upper-Tail


H0: 渭 鈮?渭0 H1: 渭 %26gt; 渭0





hypothesis test (lower or upper) = lower








Step 2: Determine a planning value for 伪 [level of significance] = 0.1





Step 3: From the sample data determine x-bar, s and n; then compute Standardized Test Statistic: t = (x-bar - 渭0)/(s/SQRT(n))





x-bar: Estimate of the Population Mean (statistical mean of the sample) = 19


n: number of individuals in the sample = 5


s: sample standard deviation = 4


渭0: Population Mean = 21


significant digits = 3





Standardized Test Statistic t = ( 19 - 21 )/( 4 / SQRT( 5 )) = 1.118








Step 4: Using Students t distribution, "lookup" the area to the left of t (if lower-tail test) or to the right of t (if upper-tail test) using Students t distribution Table or Excel TDIST(x, n-1 degrees_freedom, 1 tail).


=TDIST( 1.118 , 4 , 1 )





Step 5: Area in Step 4 is equal to P value = 0.163


based on n -1 = 4 df (degrees of freedom).





Table look-up value shows area under the 4 df curve to the left of t = 1.118 is (approx) probability = 0.163





Step 6: For P 鈮?伪, fail to reject H0; and for P %26lt; 伪, reject H0 with


90% confidence.





Conclusion: H0 is true





Note: level of significance [伪] is the maximum level of risk an experimenter is willing to take in making a "reject H0" or "conclude H1" conclusion (i.e. it is the maximum risk in making a Type I error).