Question

Nine experts rated two brands of coffee in a​ taste-testing experiment. A rating on a​ 7-point scale ​(1equals extremely ​unpleasing, 7equals extremely ​pleasing) is given for each of four​ characteristics: taste,​ aroma, richness, and acidity. The accompanying data table contains the ratings accumulated over all four characteristics. Complete parts​ (a) through​ (d) below.

Expert Brand A Brand B

C.C. 25 26

S.E. 26 26

E.G. 19 22

B.I. 22 24

C.M. 19 21

C.N. 25 26

G.N. 27 26

R.M. 24 26

P.V. 19 21

a. The test statistic is

​(Type an integer or a decimal. Round to two decimal places as​ needed.)

b. What assumption is necessary about the population distribution in order to perform this​ test?

c. Determine the​ p-value in​ (a) and interpret its meaning.

d.Construct a 95​% confidence interval estimate of the difference in the mean ratings between the two brands. Recall that mu Subscript Upper DμDequals=mu 1 minus mu 2μ1−μ2​, where mu 1μ1 is the mean rating for brand A and mu 2μ2 is the mean rating for brand B.

Answer 1

using excel>addin>phstat<two sample test>pooled variance test

we have

Pooled-Variance t Test for the Difference Between Two Means
(assumes equal population variances)
Data		Confidence Interval Estimate
Hypothesized Difference	0		for the Difference Between Two Means
Level of Significance	0.05
Population 1 Sample			Data
Sample Size	9		Confidence Level	95%
Sample Mean	22.88888889
Sample Standard Deviation	3.218867986		Intermediate Calculations
Population 2 Sample			Degrees of Freedom	16
Sample Size	9		t Value	2.1199
Sample Mean	24.22222222		Interval Half Width	2.7870
Sample Standard Deviation	2.279132389
			Confidence Interval
Intermediate Calculations		Interval Lower Limit	-4.1203
Population 1 Sample Degrees of Freedom	8		Interval Upper Limit	1.4537
Population 2 Sample Degrees of Freedom	8
Total Degrees of Freedom	16
Pooled Variance	7.7778
Standard Error	1.3147
Difference in Sample Means	-1.3333
t Test Statistic	-1.0142
Two-Tail Test
Lower Critical Value	-2.1199
Upper Critical Value	2.1199
p-Value	0.3256
Do not reject the null hypothesis

a. The test statistic is -1.01

b the necessary assumption about the population distribution in order to perform this​ test is that the sample should be drawn from the normally distributed population .

c. the​ p-value is 0.3256 which is large so we can sa that there is no difference​ in the mean ratings between the two brands.

d.a 95​% confidence interval estimate of the difference in the mean ratings between the two brands. is -4.1203 to 1.4537