06 CHE 315 HW6-Hypothesis testing(1) Home Insert Page Layout Formulas Data Revie

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Question

06 CHE 315 HW6-Hypothesis testing(1) Home Insert Page Layout Formulas Data Review View Wrap Text Arial B 1 u, .. 3,-, E .. Merge & Center. $. % , .00 conditional Forable Styles Formatting as Table Styles 13 371202535 9.073732817 11 62291349 13.56349149 12 85249293 14.86431774 14.6880657 1651114988 19 Can you conclude that the mean of this data set is greater an 11? Use the appropriate hypothesis test Use an alpha of 0 05 Be sure to clearly state the null and alternative hypotheses 20Dothismanually by calculating the Seet satistic and comparing to the ortical value You may then use buit in functions or the XLminer Analysis Toopak to check your resuts. 8.853601712 15.1452545211.151340 13.58139079 8.657948387 12.6622433 662952804 15 05779043 1227691305 4.6889657 16.51114988 6 876353718 9073732817 11.62291349 13 563491491285249293 4.86431774 27 0 Problem 32 Can you conclude that there is a real dference beteeen X and Y? Use the appropriate hypothesis test. Use an alpha of 0,05.Be sure to clearly state the null and aternative 34 by caloulating he best statstic and compering to the nal ae You may then use built in functions or the XLminer Aralysis Toolpak to check your results 5 5006091 13.7628952218.03904797 1551945829 1376209522 1185891717 102m2622 1556644435 3594599 15.08320315 14.39105637 10.80907se6 13.86463982 21.39558772 56801001 12 02397485 14.75107524 4 6794575 15.7938972 3 064/62663 13 7458804716.92595762 7.10458554 20 2976106 9 35760437912.65151937 1 10.34 194836 12 25422838 1512415877 951867557 11858717 15.89072992 10.78407177 1 14 3025006 15.93867424 12.2033809 10 22832622 13.99488039 262792271 5 83615013 2.12441189 12.18624074 18.77542588 19.3584599 18.34314565 16.65182187 4 8217511420.48136916 15.58844435 1 1177001117 9.905112875 10.5547892 10.121299se 5.838637434 11.51012868 11.76758143 7 1.4812328110 5021003116.76237555 12.58014609 6.1138337212 21679045 12 548307561 1 06819674 6.596124654 4 888655711.4374398868856638465 13 36174883 16614044329.413674637 8 853601712 1.40694938 10.49083291 12 58209546 1 93683421 16.71547626 13 93784335 14.11894487 7788938153 7317429767 10.16603397 11.33574022 3439213.58139079 7.3712026356.876353718 907373281711.62291349 11.10582318 .14525452 111513439213 58139079 8657948387 12 86292433 9 10 67265639 1285222422 1240920101 11.1622107 9.662952894 1505779943 12 27891305 16 51114988 149 12 85249293 14.86431774 14.6889657 51 Can ·codade that there is a real drierenoe between X and Y? Use the spproprate hyponess test use an apra or oosBo sue todeary state the nul and aternasve hyponeses Dthismanuslly by calculating the teet statistie and comparing to the critical value. You may then use buit in functions or the XLminer Analysis Toolpak to check your resuts Hw6

Explanation / Answer

Let xi = ith given observation. i = 1, 2, …., 18

We assume X ~ N(µ, 2) where we want to test if µ > 11 and 2 is unknown.

Claim: Mean of the given set is greater than 11.

Hypotheses:

Null H0: µ = µ0 = 11 Vs Alternative HA: µ > 11

Test statistic:

t = (n)(Xbar - µ0)/s, where n = sample size; Xbar = sample average; s = sample standard deviation.

Summary of Excel Calculations is given below:

8.8536

15.1452

11.1513

13.5614

8.6579

12.6629

12.8525

15.0578

14.689

7.3712

6.8763

9.0737

11.6229

13.5635

9.663

14.8643

12.2769

16.5111

Given, n =

µ0 =

Xbar =

11.91414

s =

2.917038

tcal =

1.329555

Given =

0.05

tcrit =

1.739607

Distribution, Critical Value and p-value

Under H0, t ~ tn – 1

Critical value = upper % point of tn – 1.

Using Excel Function, tcrit = 1.74

Decision Criterion (Rejection Region)

Reject H0, if tcal > tcrit or p-value < .

Decision:

Since tcal < tcrit, H0 is accepted.

Conclusion:

There is not sufficient evidence to support the claim that the mean of the given set is greater than 11.

DONE