1) The company comes out with yet another sweetener and you want to know if any
ID: 3326433 • Letter: 1
Question
1) The company comes out with yet another sweetener and you want to know if any of these changes has changed amount of calories in the product. So you go out and collect 10 of the new packages of the product and determine that the sample mean of these is 99 calories with a standard deviation ‘s’ of 1.
a) What type of significance test would you perform between the data collected here with those collected in ‘2’ and ‘3’for the HW8 problem above (i.e. you now have three groups)?
b) Perform the test: What is the probability that the null hypothesisis true?
DATA FROM PREVIOUS TWO PROBLEMS:
https://www.chegg.com/homework-help/questions-and-answers/need-answer-two-1-cereal-company-marketing-product-contains-100-calories-want-test-hypothe-q26114712
Explanation / Answer
Q1. (a) we will perform the ANOVA test here as there are more than 2 groups now. We will perform one way ANOVA analysis here where the hypothesises are
H0 : All three sweetner has same mean calorie level among three type of sweetner.
Ha : At least one of the sweetner has different calorie level than the other two.
Here summary of all three groups are given below.
Grand Mean xGM = (102 + 104 + 99)/3 = 101.67
SSW = n (x - x)2 = 10 * [(102 - 101.67)2 + (104 - 101.67)2 + (99 - 101,67)2] = 126.67
dF(Within treartments) = 2
MSW = 126.67/2 = 63.335
SSE = (n -1)s2 = 9 * [1 + 16 + 1] = 162
dF(error) = 27
MSE = 162/27 = 6
F = MSW/MSE = 63.335/6 = 10.5555
Here p- value = FDIST(10.5555; 2; 27) = 0.00041
so the probability that nullyhypothesis would be true is 0.00041 so we reject the null hypothesis and can conclude that At least one of the sweetner has different calorie level than the other two.
Groups Count Sum Average Variance STd.Dev. Column 1 10 1020 102 1 1 Column 2 10 1040 104 16 4 Column 3 10 990 99 1 1Related Questions
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