Write mu for the mean of a Normal distribution. The value of the standard deviat

Question

Write mu for the mean of a Normal distribution. The value of the standard deviation is unknown. We want to test H0: mu = 8 vs H1: mu < 8. A random sample of 15 observations is taken from this distribution, and the sample mean (x-bar) and sample standard deviation (s) are calculated. Then t = (x-bar - 8)/[s/square_root(15)] is calculated, and is found to equal = -0.85. At what levels of significance could we reject H0? 10% and 5%, but not 2.5% and 1% 10%, but not 5%, 2.5% and 1% 5%, 2.5% and 1%, but not 10% each of 10%, 5%, 2.5% and 1% None of 10%, 5%, 2.5% and 1%

Explanation / Answer

Ans:

Given that

sample size=15

so, df=15-1=14

test statistic,t=-0.85

p-value(left tailed)=tdist(0.85,14,1)=0.2048

*(we reject null hypothesis,when p-value<alpha)

Now,

alpha=0.01 or 0.025 or 0.05 or 0.1

But in above case,p-value is greater than all of the above alpha values.

So,Ho is not rejected at  10%, 5%, 2.5% and 1% significance levels.

Hence,correct option will be:

None of 10%, 5%, 2.5% and 1%

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