Answer to Question #155293 in Statistics and Probability for Kashaf

Question #155293

A random sample of n = 45 values give = 63. Can this sample be regarded as drawn from a


A normal population with mean μ = 70 and s2 =25?


1
Expert's answer
2021-01-13T19:31:49-0500

Hypothesis

H0:xˉ=70H_0:\bar x =70

H1:xˉ70H_1:\bar x \not=70

Since sample size 45>3045 >30 we use the normal distribution table



Z=xˉμs2Z= \frac{\bar x - \mu}{\sqrt{s^2}}


xˉ=63\bar x= 63

μ=70\mu=70

s2=25s^2= 25


Therefore


Z=637025=1.4Z= \frac{63 - 70}{\sqrt{25}}= -1.4

At a 95%95\% level of confidence, the sample mean can be concluded to be equal to the population mean μ=70\mu =70 if:



1.96<Z<1.96-1.96<Z<1.96

Since the Z value obtained is within the range i.e.


1.96<1.4<1.96-1.96<-1.4<1.96

We conclude that the sample is from the normal population with mean = 70 and variance = 25


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