Question

After 6 readings an individual is found to have an average red blood cell count of 25 with a sample standard deviation of 5 for a single reading. Assume that counts follow a normal distribution. A normal count is 28. Test the hypothesis that the individual is below average.

Answer 1

Data Summary

	Sample Size (n)	Mean (X̅ )	Standard Deviation (s)
Blood count	n = 6	X̅ = 25	s = 5

The null and alternative hypotheses are
Ho :  μ = 28
Ha :  μ < 28
where μ is the population mean blood count
Let the level of significance α = 0.05

We use single sample T test since population standard deviation is unknown, and sample size is small
This is a left tailed test

Using the given formulae, we get

Degrees of Freedom
df = n - 1 = 6 - 1
df = 5

t-statistic
$\newline t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}} \newline\newline\newline t=\frac{25-28}{\frac{5}{\sqrt{6}}}$
t-statistic = -1.4697

P-value
For t = -1.4697, df = 5 we find the left tailed p-value using t tables or Excel function t.dist
p-value = t.dist(-1.4697, 5, TRUE)
p-value = 0.1008

Decision
0.1008 > 0.05
that is p-value is greater than α.
Hence we DO NOT Reject Ho.

Conclusion
There does not exist enough statistical evidence at α = 0.05 to show that the individual is below average

that is,

The individual is not below average.

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