You work for a chicken soup manufacturer who believes she can introduce a differ
ID: 3221342 • Letter: Y
Question
You work for a chicken soup manufacturer who believes she can introduce a different dumpling(soy based) into her soup without affecting the incredible chicken flavor. To test this hypothesis, she produced 18 cans labeled Style "CHI" that contain the old flour based dumpling and 18 cans labeled Style "WHY" that contain the new soy based dumpling. She sends one can to each of 18 tasters and asks which they prefer, If her hypothesis is correct, we should expect 9 tasters to like CHI and 9 to like WHY. In the actual test, 11 preferred CHI, and the rest WHY. Calculate chi squared and the probability of getting a value this large or larger. Does the test indicate a significant difference between the two kinds of dumpling? Now calculate the probability exactly using the correct distribution model, and compare your results.
If you run another test with 400 cans, and 225 testers prefer CHI, has your hypothesis changed any? explain and justify.
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: The preference of CHI and WHY are same.
Alternative hypothesis: The preference of CHI and WHY are not same.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.
Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
DF = k - 1 = 2 - 1
D.F = 1
(Ei) = n * pi
(E1) = 9
(E2) = 9
2 = [ (Oi - Ei)2 / Ei ]
2 = [ (11 - 9)2 / 9 ] + [ (7 - 9)2 / 9 ]
2 = 0.4444 + 0.4444
2 = 0.8888
where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and 2 is the chi-square test statistic.
The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 0.8888.
We use the Chi-Square Distribution Calculator to find P(2 > 0.8889) = 0.345
Interpret results. Since the P-value (0.345) is greater than the significance level (0.05), we have accept the null hypothesis.
From the above test we conclude that The preference of CHI and WHY are same.
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: The preference of CHI and WHY are same.
Alternative hypothesis: The preference of CHI and WHY are not same.
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chi-square goodness of fit test of the null hypothesis.
Analyze sample data. Applying the chi-square goodness of fit test to sample data, we compute the degrees of freedom, the expected frequency counts, and the chi-square test statistic. Based on the chi-square statistic and the degrees of freedom, we determine the P-value.
DF = k - 1 = 2 - 1
D.F = 1
(Ei) = n * pi
(E1) = 200
(E2) = 200
2 = [ (Oi - Ei)2 / Ei ]
2 = [ (225 - 200)2 / 200 ] + [ (175 - 200)2 / 200 ]
2 = 3.125 + 3.125
2 = 6.25
where DF is the degrees of freedom, k is the number of levels of the categorical variable, n is the number of observations in the sample, Ei is the expected frequency count for level i, Oi is the observed frequency count for level i, and 2 is the chi-square test statistic.
The P-value is the probability that a chi-square statistic having 1 degrees of freedom is more extreme than 0.8888.
We use the Chi-Square Distribution Calculator to find P(2 > 6.25) = 0.012419
Interpret results. Since the P-value (0.0124) is less than the significance level (0.05), we cannot accept the null hypothesis.
From the above test we conclude that The preference of CHI and WHY are not same.
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