A simple random sample of 48 adults is obtained from a normally distributed popu

Question

A simple random sample of 48 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 0.54. Use a 0.01 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 limit of the range of normal values. What do the results suggest about the sample group?

Explanation / Answer

Given that,
population mean(u)=5.4
sample mean, x =5.21
standard deviation, s =0.54
number (n)=48
null, Ho: µ=5.4
alternate, H1: µ<5.4
level of significance, a = 0.01
from standard normal table,left tailed t a/2 =2.408
since our test is left-tailed
reject Ho, if to < -2.408
we use test statistic (t) = x-u/(s.d/sqrt(n))
to =5.21-5.4/(0.54/sqrt(48))
to =-2.438
| to | =2.438
critical value
the value of |t a| with n-1 = 47 d.f is 2.408
we got |to| =2.438 & | t a | =2.408
make decision
hence value of | to | > | t a| and here we reject Ho
p-value :left tail - Ha : ( p < -2.4377 ) = 0.00931
hence value of p0.01 > 0.00931,here we reject Ho

ANSWERS
---------------
null, Ho: µ=5.4
alternate, H1: µ<5.4
test statistic: -2.438
critical value: -2.408
decision: reject Ho
p-value: 0.00931

we claim that the sample is from a population with a mean less than 5.4

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.