Question

The average hemoglobin count in healthy adult females is approximately normal, with a population mean of 14. Suppose a female patient had a hemoglobin test each month last year, and the results were:

18        22        20        16        19        14

20        15        19        17        20        18

a. Find the sample mean and standard deviation.

b. At alpha = 0.01 does this indicate that this patient has a higher average than the general population?

Answer 1

Answer:

n= 12,  = 14 , = 0.01

a)

Calculate the sample mean and sample standard deviation for the sample data

we get,

Sample mean : = 18.167

Sample standard deviation : s = 2.329

b)

null and alternative hypothesis is

Ho:   = 14

H1:   > 14

c)

formula for test statistics is

t = 6.198

test statistics : t = 6.198

d)

Calculate t critical value for right tailed test with = 0.01

and df = n -1 = 12 -1 = 11

using t table we get critical values as

Critical value = 2.718

e)

decision rule is

Reject Ho if ( test statistics ) > ( Critical value)

here, ( test statistics = 6.198  ) > ( Critical value = 2.718 )

Hence,

Null hypothesis is rejected.

f)

Therefore there is sufficient evidence to support the claim that patient has a higher average than the general population.