Hypothesis testing.

rorosingsong

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Hi, I'm studying for finals atm, and I'm having difficulties with this old exam question. I would really appreciate some help here, I can't ever seem to figure out which test to use.

E. Canis is a tick borne disease of dogs which is sometimes contracted by humans. According to Vital Health Statistics (1982) the mean white blood cell count in the general human population is 72.5 (in '000/mm^3). It is believed that infection by E. Canis lowers the average white blood cell count. To investigate this, the white blood cell counts (x) of a sample of 20 infected humans was obtained:
39, 54, 50, 53, 74, 77, 78, 51, 69, 58, 87, 60, 67, 65, 70, 87, 57, 45, 61, 71.

Set up appropriate null and alternative hypotheses, and perform a test of significance which assumes normality.

I've already calculated the sample mean (63.65) and sample standard deviation (13.22), but have no idea where to go from there. Please help!
Thanks in advance!

Roro
 
Because there are 20 samples, this is a t-test.

The hypothesis would be to test if the mean cell count is indeed lower with the disease, as the claim suggests.

\(\displaystyle H_{0}: \;\ \mu<72.5, \;\ \text{claim}\)

\(\displaystyle H_{a}: \;\ \geq 72.5\)

There are 19 degrees of freedom. Going to the t table using left tail with \(\displaystyle \alpha=.05\),

the critical value is -1.729

But, our test statistic is \(\displaystyle t=\frac{(63.65-72.5)\sqrt{20}}{13.22}=-2.99\)

We are in the rejection region, so we reject the null hypothesis. This means there is not enough evidence at the .05 level to support the claim that the cell count is lower with the disease.

Also note that the p value is .00374

Since this is lower than our alpha level, we reject the null hypothesis.
 
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