04. (2-Sample t test) A test engineer at NASA decides to sample four wheel proto
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04. (2-Sample t test) A test engineer at NASA decides to sample four wheel prototypes from production line 1 and measure the diameter of each wheel in inches. The table below shows her results: Wheel number Wheel diameter (inches) 12.64 15.73 12.45 11.74 2 She also samples three other prototypes from production line 2 (which is independent of line 1), and obtains the following results: Wheel number Wheel diameter (inches) 5 6 14.05 13.02 14.22 A Compute the difference of means z = x1 x2 of the above two samples. Round your answer to two decimal places. (a) -0.62 (b) -0.16 (c) -0.46 (d) -1.49 B) Compute the pooled standart cerror n+ of the above two samples. Round your final 8 answer to two decimal places. (a) 0.83 (b) 0.94 (c) 0.96 (d) 0.85 C) What hypotheses should she test if she suspects that the true mean diameter, ui of the popu- lation of prototypes from line 1 is not the same as the true mean diameter, 2 of the population of prototypes from line 2? (i.e., that the true difference of means, 1-2 is not zero)Explanation / Answer
> production1=c(12.64,15.73,12.45,11.74)
> production2=c(14.05,13.02,14.22)
A)> mean(production1)-mean(production2)
[1] -0.6233333
Option(a)
B)> sqrt(sd(production1)^2/4+sd(production2)^2/3)
[1] 0.9609342
Option(c)
C)According to the question, the hypotheses will be option (a).
D) Range of p-value : p-value > 0.05. All options are wrong.
E)> t.test(production1,production2,paired=F)
Welch Two Sample t-test
data: production1 and production2
t = -0.64867, df = 3.9814, p-value = 0.5521
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-3.296242 2.049575
sample estimates:
mean of x mean of y
13.14000 13.76333
Since p-value>0.05, the true difference is not significantly other than zero. Option(b)
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