Question

Canis infection is a tick-borne disease of dogs that is sometimes contracted by humans. In the general population, white blood cell count is normally distributed with a mean of 7250/mm3. It is believed that persons infected with E. canis must on average have a lower white blood cell count. For a sample of 15 infected persons, the mean white blood cell count is 4767/mm3 and the standard deviation is 3204/mm3.

a) Conduct a two-sided test at the alpha = 0.01 level to determine whether those who are infected have lower white blood cell counts.
b) Now, create a confidence interval based on the equivalent criteria (i.e.significance level) as was used in part a)

Answer 1

To evaluate the effect of E. canis on white blood cell count, a two-sided hypothesis test can be performed at an alpha level of 0.01, and a 99% confidence interval can be constructed using the given sample data and the t-distribution.

Step-by-step explanation:

When assessing the impact of E. canis, an obligatory intracellular bacteria transmitted by ticks causing ehrlichiosis, on the white blood cell count in humans, we can perform a two-sided hypothesis test and construct a confidence interval to analyze the data.

Two-sided Hypothesis Test

To conduct a two-sided test at the alpha = 0.01 level, we first establish our null hypothesis (H0) that there is no difference in the white blood cell count for those infected with E. canis as compared to the general population, against the alternative hypothesis (H1) that there is a significant difference. Using the provided sample mean, standard deviation, and sample size, we can calculate the test statistic assuming a normal distribution, comparing it to the critical value from the standard normal distribution at the 0.01 significance level. If the absolute value of the test statistic exceeds the critical value, we reject the null hypothesis.

Confidence Interval

Now, to create a confidence interval at the same significance level, we utilize the sample mean and standard deviation to estimate the range within which the true mean white blood cell count for infected individuals is likely to fall. The 99% confidence interval can be calculated using the t-distribution, given the small sample size, to estimate the margin of error and then applying it to the sample mean.