Question

Nine experts rated wo brands o coffee in a aste esing experiment. A rating on a 7-port scale extremely unpleasing. 7 = extremely pleasing is given or each o our characteristics: aste, aro ma nchness and ac dit The accompanying data table contains the ratings accumulated over all four characteristics. Complete parts (a) through (d) below. EEB Click the icon to view the data table. a. At the 0.01 level of significance, is there evidenoe of a difference in the mean ratings between the two brands? Let μ1 be the mean rating for brand A and μ2 be the mean rating for brand B. Determine the null and alternative hypotheses for this test. The test statistic is tsTAT Type an integer or a decimal. Round to two decimal places as needed.) The critical value(s) is(are) or decimals. Round to two decimal places as needed. Use a comma to separate answers as needed.) Ho. There is Since the test statistic b. What assumption is necassary about the population distribution in order to perform this test? OA. It must be assumed that the distribution of the differences between the measurements is skewed the critical value(s). evidence to conclude that the mean ratings are different between the two brands. B. It must be assumed that the distribution of the differences between the measurements is approximately uniform.

Answer 1

Claim : There is difference in the mean ratings between the two brands.

Option C H₀: µ_d = 0    vs H_a: µ_d ≠ 0

   We can use TI-84 calculator to perform paired t test.

First find the differences d = Brand A - Brand B

d-10322-11-1-1 1 B 25 24 2 2 2 2 221

First enter the differences d in the column L1.

TI-84 Plus Silver Edition TEXAS INSTRUMENTS 司 1L2 1L3 1 1 LI ={-1.0, -3.-2. STAT PLOTF1 TBLSETF2 FORMATF3 TABLE F5 CALC F4

Then press STAT ---> scroll to TESTS ---> Select T test and hit enter.

TI-84 Plus Silver Edition TEXAS INSTRUMENTS EDIT CALC 1 : Z-Test T-Test 2-SamPZTest 4:2-SamPTTest... 5: 1-PrOPZTest... 6:2-ProFZTest... 7↓Z Interval.. STAT PLOTF1 TBLSETE2 FORMAT F3 TABLE FS CALC F4

Select Data and hit enter , plug the values accordingly.

For List : L1 ( Press 2ND key then 1 )

TI-84 Plus Silver Edition やTEXAS INSTRUMENTS T-Test Inpt Lata Stats LIat ListiL1 Fre : 1 Calculate Draw STAT PLOT F1 TBLSETF2 FORMAT F3 TABLE FS CALC F4

Scroll to calculate and hit enter

TI-84 Plus Silver Edition TEXAS INSTRUMENTS T-Tst μ#8, 0000 t--2.8571 E=" 0212 Sx=1. 1667 n=9.0000 STAT PLOT F1 TBLSETF2 FORMAT F3 TABLE F5 CALC F4

t Stat = -2.86

Critical value =

Press 2ND ---> VARS ---> Select invT() and hit enter

TI-84 Plus Silver Edition やTEXAS INSTRUMENTS DRAW hormalrat 2i normalcdf STAT PLOTF1 TBLSETF2 FORMAT F3 CALC F4 TABLE F5

We are given α =0.01 , so area = 0.01/2 and df = n-1 = 9-1 = 8

TI-84 Plus Silver Edition 9 TEXAS INSTRUMENTS nyT area 0.01 2 Paste STAT PLOTF1 TBLSETF2 FORMATF3 CALC F4 TABLE F5

やTEXAS INSTRUMENTS 3. 3554

This is two tail test therefore critical values are -3.36 , 3.36

Since test statistic fall between the critical values , we do not reject H0 , There is no sufficient evidence to conclude that the mean ratings are different.

b) Assumption :

c . The distribution of differences between the measurements is approximately normal.

C) p - value = 0.021

Interpretation of p value : B

D) 99% confidence interval :

Press STAT ---> scroll to TESTS ---> Select T interval and hit enter.

TI-84 Plus Silver Edition やTEXASINSTRUMENTS EDIT CALC I嵁 2TT-Test 3:2-SamPZTest... 4:2-SampTTest... 5: 1-ProFZTest... 6:2-PrOFZTest... 7:ZInterval.. UTInterval.. STAT PLOTF1 TBLSETF2 FORMATF3 TABLE F5 CALC F4

For List : L1 ( Press 2ND key ---> 1 )

C-level : = 0.99

TI-84 Plus Silver Edition TEXAS INSTRUMENTS Inpt L L1st L1 Freg:i C-Level:.99 Calculate Stats STAT PLOTF1 TBLSETF2 FORMATF3 CALC F4 TABLE F5

やTEXAS INSTRUMENTS -2.416,.1938 Sx 1.1667 Interval n=9, 0000 STAT PLOTF1 TBLSETF2 FORMAT F3 TABLE F5 CALC F4

So 99% confidence interval is ( -2.42 , 0.19 )