determine the critical value. determine the degrees of freedom n-1. t stat: Nine

Question

determine the critical value.
determine the degrees of freedom n-1.
t stat:

Nine experts rated two brands of coffee in a taste testing experiment A rating on a 7-point scale (1 -extremely unpleasing, 7-extremely pleasing) is given for each of four characteristics: taste, aroma, nchness, and acidity. The accompanying data table contains the ratings accumulated over all four characteristics. Complete parts (a) through (d) below E Click the icon to view the data table. a. At the 0.10 level of significance, is there evidence of a difference in the mean ratings between the two brands eth, be the mean rating for brand A and 2 be the mean rating for brand B. Determine the null and atternative hypotheses for this test

Explanation / Answer

Null Hypothesis

H0: u1 - u2 = 0, where u1 is the mean of first population and u2 the mean of the second.

As above, the null hypothesis tends to be that there is no difference between the means of the two populations; or, more formally, that the difference is zero

t statistics for the two sample,

Difference Scores Calculations

Treatment 1

N1: 9
df1 = N - 1 = 9 - 1 = 8
M1: 23.67
SS1: 60
s21 = SS1/(N - 1) = 60/(9-1) = 7.5


Treatment 2

N2: 9
df2 = N - 1 = 9 - 1 = 8
M2: 23.67
SS2: 152
s22 = SS2/(N - 1) = 152/(9-1) = 19


T-value Calculation

s2p = ((df1/(df1 + df2)) * s21) + ((df2/(df2 + df2)) * s22) = ((8/16) * 7.5) + ((8/16) * 19) = 13.25

s2M1 = s2p/N1 = 13.25/9 = 1.47
s2M2 = s2p/N2 = 13.25/9 = 1.47

t = (M1 - M2)/(s2M1 + s2M2) = 0/2.94 = 0

t critical value in excel is t.inv(0.01,16)=-2.58

so here we fail to reject the null hypothesis.

Assumption of two sample t-test

here p-value is 1, so we fail to reject the null

The formula for confidance interval is,

1 - 2 = (M1 - M2) ± ts(M1 - M2)

where:

M1 & M2 = sample means
t = t statistic determined by confidence level
s(M1 - M2) = standard error = ((s2p/n1) + (s2p/n2))

Pooled Variance
s2p = (SS1 + SS2) / (df1 + df2) = 26.21 / 16 = 1.64

Standard Error
s(M1 - M2) = ((s2p/n1) + (s2p/n2)) = ((1.64/9) + (1.64/9)) = 0.6

Confidence Interval
1 - 2 = (M1 - M2) ± ts(M1 - M2) = 0 ± (2.12 * 0.6) = 0 ± 1.2791

1 - 2 = (M1 - M2) = 0, 95% CI [-1.2791, 1.2791].

You can be 95% confident that the difference between your two population means (1 - 2) lies between -1.2791 and 1.2791.

thannk you

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