A simple random sample of 59 adults is obtained from a normally distributed popu

Question

A simple random sample of 59 adults is obtained from a normally distributed population, and each person's red blood cell count (in cells per microliter) is measured. The sample mean is 5.21 and the sample standard deviation is 0.51. Use a 0.05 significance level and the given calculator display to test the claim that the sample is from a population with a mean less than 5 4, which is a value often used for the upper of the range of normal values. What do the results suggest about the sample group?

Explanation / Answer

Set Up Hypothesis
Null, H0: U = 5.4
Alternate, H1: U<5.4
Test Statistic
Population Mean(U)=5.4
Sample X(Mean)=5.21
Standard Deviation(S.D)=0.51
Number (n)=59
we use Test Statistic (t) = x-U/(s.d/Sqrt(n))
to =5.21-5.4/(0.51/Sqrt(59))
to =-2.862
| to | =2.862
Critical Value
The Value of |t | with n-1 = 58 d.f is 1.672
We got |to| =2.862 & | t | =1.672
Make Decision
Hence Value of | to | > | t | and Here we Reject Ho
P-Value :Left Tail -Ha : ( P < -2.8616 ) = 0.00293
Hence Value of P0.05 > 0.00293,Here we Reject Ho

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