C D 45 47 50 51 61 62 75 74 25 27 37 40 55 54 90 92 100 103 15 14 22 25 18 19 Us
ID: 3050012 • Letter: C
Question
C D
45 47
50 51
61 62
75 74
25 27
37 40
55 54
90 92
100 103
15 14
22 25
18 19
Use Columns C and D for this question.
You are measuring weights using two different scales C and D. You want to know whether there is any difference in the weight depending on which scale is used. Column C gives the weight using scale C. Column D gives the weight for the SAME object using scale D. Now there are two ways to do the problem. We could test if µ(C) is equal to µ(D). Or since there is data for the same object using different scales, we could test whether µ(C-D) = 0.
The better way to do this problem is to test whether µ(C-D) = 0, or µ(C-D) 0 since we have correlated data.
Make a new series of data samples by letting E = C – D. List your new series of 12 numbers.
What is the null hypothesis H0 ?
What is the alternative hypothesis Ha ?
What type of tail test are we going to use? (left tail, right tail, two tail)
What is the mean xbar of this new sample?
What is the standard deviation of the sample s?
What is the size of the sample n?
How many degrees of freedom does this data set have?
What is the t-statistic for this sample?
Use the t-distribution calculator to compute a p-value. Show a screen shot of your answer.
Based on this value of p and using a 90% confidence level, is there a systematic difference in the weights as measured by the scales? Should we accept or reject the null hypothesis?
Explanation / Answer
this is two tailed test
n=12
As p-value is less than significance level of 0.05, we reject null hypothesis.
There are significant evidence that there is systematic difference in the weights as measured by the scales
C D dbar(E) 45 47 -2 50 51 -1 61 62 -1 75 74 1 25 27 -2 37 40 -3 55 54 1 90 92 -2 100 103 -3 15 14 1 22 25 -3 18 19 -1Related Questions
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