Question

Prob1 Company A 52098.70805 50981.26776 59275.73435 53082.52597 53886.08272 51668.41772 53138.68242 54356.09171 59544.14955 53937.52316 56636.40834 54516.06871 56651.47495 57049.69624 51731.51989 58327.5357 56764.35505 54637.43023 54619.77234 55933.42172 62849.00252 55636.94172 58552.53464 57194.07848 55935.2954 60381.38829 58829.88221 58775.87227 49138.51243 55732.81523 54112.14668 56213.34338 54749.80985 57893.66632 60073.07422 57158.72958 54690.05094 56096.40651 56708.00854 57944.54452 Prob1 Company B 45538.63529 49210.84057 47041.85444 44146.62261 41016.85498 44832.95939 42020.39638 51084.90005 42815.50348 51114.69983 47064.11355 45099.4801 49341.83439 39780.31581 47581.18386 45650.69784 44953.48972 47598.91067 42087.00787 40926.06123 47425.41306 43214.68775 50967.80611 44451.33893 47656.8827 48562.98213 42730.81243 49953.79874 41401.47422 44640.92484 47174.44517 46101.41375

Answer 1

Part a)

Claim : Tires of company A outlast the tires of company B by more than 10000 miles

H0:  µ_A -  µ_B = 10000

Ha : µ_A -  µ_B > 10000

We can find the sample means and sample sd of the given data set using excel functions =AVERAGE(data set column range )

and =STDEV.S( data set column range ) respectively.

So sample mean for company A = $\bar{X}$ ₁ = 56064.66

sample SD for company A = S₁ =2748.69

sample size for company A = n₁ = 40

sample mean for company B = $\bar{X}$ ₂ = 45724.64

sample SD for company B = S₂ = 3176.60

sample size for company B = n₂  = 32

We can use the Ti-84 calculator to find the Test statistic and p value :

Press STAT ---> Scroll to TESTS --> Select 2-sample T test and hit enter

Then select Stats and hit enter. then plug the values accordingly

While entering the value for $\bar{X}$ 1 subtract 10000 , since we have difference    µ_A -  µ_B = 10000

So plug $\bar{X}$ ₁ = 46064.66

Select the sign at Ha , for pooled : select Yes and hit enter

Then scroll to calculate and hit enter

So Test statistic = 0.49

P-value = 0.3140

Conclusion : As p-value is greater than α =( 0.05) , we fail to reject H0

Part b) we are asked to find 98% confidence interval for  µ_A -  µ_B

We can use function 2- sample T Interval in TI-84 calculator .

Press STAT ---> Scroll to TESTS --> scroll down to 2-sample T Interval and hit enter.

Then select Stats and hit enter. then plug the values accordingly

For confidence interval plug the calculated value of   $\bar{X}$ ₁ = 56064.66

Plug C- Level = 0.98 and for pooled : select Yes and hit enter

Then scroll to calculate and hit enter

Therefore 98% confidence interval for  µ_A -  µ_B is ( 8676.6 , 12003 )