Question

Assume that both populations are normally distributed. ​(a) Test whether mu 1 not equals mu 2μ1≠μ2 at the alpha equals 0.01α=0.01 level of significance for the given sample data.​(b) Construct a 99​% confidence interval about mu 1 minus mu 2μ1−μ2.			Population 1	Population 2
		n	13	13
		x overbarx	13.9	11.2
		s	3.1	2.8

Answer 1

i am using minitab to solve the problem.

Summarized data ;-

copy the data in minitab stat basic statistics 2 sample t select summarized data in sample 1 type13 in sample size, 13.90 in sample mean, 3.10 in standard deviation in sample 2 type 13 in sample size, 11.2 in sample mean, 2.80 in standard deviation options in confidence level type 99 in hypothesized difference type 0 select the alternative hypothesis as difference hypothesized difference ok ok.

*** SOLUTION ***

a).hypothesis:-

[ claim ]

the test statistic (z) = 2.33

p value = 0.0289

decision:-

p value = 0.0289 > 0.01(alpha)

we fail to reject the null hypothesis.

b).the 99% confidence interval = (-0.55 , 5.95)

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