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The population µ = 5. The sample data is 1, 1, 2, 4, 4. a) Calculate...

The population µ = 5. The sample data is 1, 1, 2, 4, 4.

a) Calculate a single-sample t statistic.

b) Find the critical values for the critical regions.

c) Draw a conclusion.

d) Calculate the confidence interval.

e) Calculate Cohen’s d.

math   Statistics-And-Probability   
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Answer #1

Here~we~want~to~test~H_0:\mu=5~vs.~H_1:\mu\neq 5 \\n=5,~x_1=1,~x_2=1,~x_3=2,~x_4=4,~x_5=4,~\bar{x}=\frac{1}{5}(1+1+2+4+4)\\ =2.4,~\sum_{i=1}^5x_i^2=1^2+1^2+2^2+4^2+4^2=38 ,~s=\sqrt{\frac{1}{4}\sum_{i=1}^5x_i^2-\frac{5}{4}\bar{x}^2}=1.52,\\ a.~t=\frac{\sqrt{5}(\bar{x}-5)}{s}=-3.82\\ Test~statistic=-3.82\\ b.~critical~region:~|t|>t_{4,0.025}=2.78\\ c.~|t|=3.82,~hence~we~reject~H_0~at~0.05~\\ level~and~conclude~that~population~mean~is~different~from~5.\\ d.~95\%~C.I.~of~\mu~is\\ (\bar{x}-2.78\times \frac{s}{\sqrt{5}},~\bar{x}~2.78\times \frac{s}{\sqrt{5}})=(0.51,~4.29)

e. Cohens d = t/ 5 3.82/ /5 =-1.71

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