**So I've got a couple questions on my stats homework as follows:**

E. Canis infection is a tick-bone disease of dogs that is sometimes contracted by humans. Among infected humans, the distribution of WBC counts has an unknown mean u and a SD o. In the general population, the mean WBC count is 7250/mm3. It is believed that persons infected with E. Canis must on average have lower WBC counts.

a) What are the null and alternative hypotheses for a one-sided test?

b) for a sample of 15 infected persons, the mean white blood cell count is

X(bar) = 4767/mm3 and the standard deviation is s=3204/mm3. Conduct the test at the α = 0.05 level (This is a one-sided test)

d) calculate a p-value

e) repeat parts b, c and d using two-sided testing and comment on the differences in the results that you get.

E. Canis infection is a tick-bone disease of dogs that is sometimes contracted by humans. Among infected humans, the distribution of WBC counts has an unknown mean u and a SD o. In the general population, the mean WBC count is 7250/mm3. It is believed that persons infected with E. Canis must on average have lower WBC counts.

a) What are the null and alternative hypotheses for a one-sided test?

b) for a sample of 15 infected persons, the mean white blood cell count is

X(bar) = 4767/mm3 and the standard deviation is s=3204/mm3. Conduct the test at the α = 0.05 level (This is a one-sided test)

d) calculate a p-value

e) repeat parts b, c and d using two-sided testing and comment on the differences in the results that you get.

a) H0: u < (or equal to) 7250/mm3

HA: u > 7250/mm3

I think I understand that I have to calculate a one-sided test for b & c the first time around, then a 2-sided test for b & c. Here are my calculations for the test statistic for the one sided test

b) t = [X(bar) - u] / [s/(sqrt)n]

t = [4767 - 7250] / 3204 / (sqrt)15

t = -2483 / 827.2692

t = -3.001

Then, determine the critical regions:

-tn-1, 0.05

-t15-1.05

-t = -(infinity) to -2.145

therefore, we can reject the null because the value of -3.001 is within the critical region?

OR, should I be doing something like a 95% confidence interval, like I've done below?

X(bar) +/- t n-1, 0.025 x (standard error)

95% CI = 4767 +/- 2.145 x 2304/(sqrt)15

95% CI = 4767 +/- 1276.0395

95% CI = (6043.0395 , 3490.9604)

I hope that this is clear enough

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