Answer to Question #150243 in Statistics and Probability for Alex

Question #150243
Machine A and machine B produce identical components and it is required to test if the mean diameter of the components is the same. A random sample of 144 from machine A had a mean of 36.4 mm and a standard deviation of 3.6 mm; whilst a random sample of 225 from machine B had a mean of 36.90 mm and a standard deviation of 2.9 mm.
Are the means significantly different at the 5% level?
1
Expert's answer
2020-12-11T14:06:50-0500

Solution


"H_0: \\mu_1- \\mu_2=0" vs

"H_1: \\mu_1-\\mu_2 \\not= 0"


Test statistic :


"Z-test= {(\\bar{x}_1 - \\bar{x} _2)-(\\mu_1 - \\mu_2) \\over \\sqrt {{S_1^2\\over n_1}+{S_2^2 \\over n_2}} }"

"={(36.4-36.90)-0 \\over {\\sqrt{{3.6^2 \\over 144}+{2.9^2 \\over 225}}} }"

"=-1.400"

Z-value:

"Z_{0.025}=1.96 \\space and \\space - 1.96"


Since the test statistic lies between -1.96 and 1.96, we fail to reject the null hypothesis.

Therefore there is no sufficient evidence to support the claim that the machine A is significantly different from machine B.


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