Question

(1 point) There has been an alcohol war between Bob and Len for some time now. The following results were observed. Does the data indicate that the average purchases at LenÃcACA s exceed, on average, those at BobAcÃCA s by more than 8.50 dollars? The data is given in the file below. Minitab File And is summarized here Bobs Booze Lens Liquor Emporium 46 39 average cost variance of cost 52.52 61.9 6.99 2.08 (a) Form the correct hypothesis A. Ho HLen=Bob HA HLen< HBob ОВ. Но : иет 3D И Воb НА: MLen # M Bob C. Ho Len Bob = 8.5 HA: HLen-Bob# 8.5 D. Ho : иLen И Воb НА: нLen > И Bob ОЕ. Но : иLen - И Воb — 8.5 OF. Но : MLen — M Воb 3D 8.5 НА: HLen - И Воb < 8.5 На: HLen - H Воb > 8.5 (b) Using technology available to you, test to see if the variances are equal or not? A. There appears to be more variation in Bobs sales than in the Lens O B. They appear to be equal There appears to be more variation in Lens sales than in the Bobs. (b) (i)Report the p-value of the test you ran in (b)) use three decimals in your answer. P-value (c) Test the statistical hypotheses in (a) by carrying out the appropriate statistical test. Find the value of the test statistic for this test, use two decimals in your answer Absolute value of the test statistic (d) Determine the P-value for the difference of means test, and report it to three decimal places. P = (e) Determine the appropriate degrees of freedom for this test. As an integer DF the null hypothesis. Use a = 0.045 ()Based on the above calculations, we should

Answer 1

a)
option F) is correct

b)

i)

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: o Ha o This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used (2) Rejection Region Based on the information provided, the significance level is a 0.05, and the the rejection region for 1.873} {F: F < 0.543 or F this two-tailed test is R (3) Test Statistics The F-statistic is computed as follows: 6.99 = 3.361 2.08 (4) Decision about the null hypothesis Since from the sample information we get that F 3.361 > Fu = 1.873, it is then concluded that the null hypothesis is rejected. (5) Conclusion It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population variance o is different than the population variance o, at the a 0.05 significance level.

option A)

b) ii)

p-value = 0.000

c)

Two sample T summary hypothesis test: P1 Mean of Population 1 H2 Mean of Population 2 H1 H2 Difference between two means Ho H H2 8.5 HA HH2 8.5 (without pooled variances) Hypothesis test results: Difference Sample Diff. Std. Err. P-value DF T-Stat 9.38 0.45308909 71.675491 1.9422229 0.028

TS = 1.94

d)

p-value = 0.028

e)

DF = 72
f)

we reject the null as p-value < alpha