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# Two Tailed Test of Hypothesis

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In a normal population with sigma=20, a random sample of size n gave X(mean)=56.53. At the 5% significance level, make a two-tailed test of the null hypothesis mu=50, when (a) n=24 (b) n=36.

In each case report the P value.

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#### Solution Preview

Since the population standard deviation is known we will use z table in both cases.
(If it was not known then we would have used t table for sample sizes less than 30 in this case in part a)

a)

Hypothesized Mean=M = 50
Standard deviation =s= 20
sample size=n= 24
sx=standard error of mean=s/square root of n= 4.0825 = ( 20 /square root of 24)
Significance level=alpha (a) = 0.05
No of tails= 2
This is a 2 tailed test because we ...

#### Solution Summary

Two tailed test of hypothesis have been carried out for different sample sizes.

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