In a packing plant, a machine packs cartons with jars. It is hypothesized that t
ID: 3231237 • Letter: I
Question
In a packing plant, a machine packs cartons with jars. It is hypothesized that the old machine will pack slower on average (that is, have a higher average time) than the new machine. To test that hypothesis, a researcher collected a sample from both machines and recorded the time each machine took to pack a carton. The following table shows the sample data summary collected from the two machines.
Assume that the p-value is 0.04(Prob > t = 0.04, Prob < t = 0.96 and Prob > |t| = 0.08). Suppose now the researcher is interested to build condence interval of the dierence between new machine population mean packaging time and old machine population mean packaging time. Which is the largest condence interval which will not contain 0?
a) 3%
b) 80%
c) 90%
d) 95%
Data Summary Machine Sample Std Dev Sample Size Sample Mean New 35 13.80 2257 42 Old 11.70 5.21Explanation / Answer
The 95% confidence interval is thw widest interval not including 0
n1 = 35
n2 = 42
x1-bar = 13.8
x2-bar = 11.7
s1 = 2.57
s2 = 5.21
% = 95
Degrees of freedom = n1 + n2 - 2 = 35 + 42 -2 = 75
Pooled s = (((n1 - 1) * s1^2 + (n2 - 1) * s2^2)/DOF) = (((35 - 1) * 2.57^2 + ( 42 - 1) * 5.21^2)/(35 + 42 -2)) = 4.222913212
SE = Pooled s * ((1/n1) + (1/n2)) = 4.22291321246364 * ((1/35) + (1/42)) = 0.966493308
t- score = 1.992102124
Width of the confidence interval = t * SE = 1.99210212378202 * 0.966493307936332 = 1.925353371
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