A new design in shipping containers for ampoules is compared to the existing one
ID: 3314349 • Letter: A
Question
A new design in shipping containers for ampoules is compared to the existing one to determine if the number of broken units can be reduced. One hundred shipping containers of each design are subjected to identical rigorous abuse and failures are defined as broken ampoules in excess of 1%. The results of this study are presented in Table 2.
Table 2. Data Comparing Two Container Designs
Results
New Container
Old Container
Total
Success
97
88
185
Failure
3
12
15
Totals
100
100
200
2. a. State the null hypotheses
2. b. State the alternative hypotheses
2. c. What is the degree of freedom (df)?
2. d. What is the critical value for that df assuming = .05?
2. e. Compute the test statistic, 2, using the short-cut formula.
2. f. Do the data suggest the design is an improvement over the one currently used?
Results
New Container
Old Container
Total
Success
97
88
185
Failure
3
12
15
Totals
100
100
200
Explanation / Answer
The Observed and expected value tables are as below:
a) The Null Hypothesis : H0: The number of broken Ampoules is the same for both designs. There is no improvement of the new design over the currently used one.
b) The Alternative Hypothesis: Ha: The number of broken Ampoules is lesser for the new design as compared to the currently used design. There is an improvement of the new design over the currently used one.
c) Degrees of freedom = (r-1) * (c - 1) = (2-1)*(2-1) = 1
d) The critical value at = .05, for df = 1 is 2critical = 3.8415
e) We can see from the tables above that the (O-E)2 value for each cell is the same = (4.5)2 = 20.25 and also 2 expected values for each row are the same.
Therefore 2observed = 2 * (20.25/92.5) + 2 * (20.25/7.5) = 2 * 0.22+ 2 * 2.7 = 0.44 + 5.4 = 5.84
f) Since 2observed (5.84) is > 2critical (3.8415), We Reject H0.
Therefore Yes, the data suggests that the design is an improvement over the one currently used.
Observed New Old Total Success 97 88 185 Failure 3 12 15 Total 100 100 200 Expected New Old Total Success 92.50 92.50 185 Failure 7.50 7.50 15 Total 100 100 200Related Questions
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