Question

An experiment was conducted to evaluate the effectiveness of a treatment for tapeworm in the stomachs of sheep. A random sample of 24 worm-infected lambs of approximately the same age and health was randomly divided into two groups. Twelve of the lambs were injected with the drug and the remaining twelve were left untreated. After 6 months, the lambs were slaughtered and the following worm counts were recorded. Assume the counts are approximately normally distributed.

Drug-treatedsheep 18 43 28 50 16 32 13 35 38 33 6 7

Untreatedsheep   40 54 26 63 21 37 39 23 48 58 23 39

(a) Construct a 98% confidence interval for the difference of the worm count in a lamb.

(b) Please perform a statistical test and see if the drug treatment reduced the mean worm count in a lamb. Use the significance level 0.05.

(c) What are your assumptions that you assumed in part (b)?

Answer 1

Using the sample data we calculate the sample mean for Drug-treated sheep and Untreated sheep and also the standard deviation for Drug-treated sheep and Untreated sheep.

	Drug-treated sheep	Untreated sheep
sample   mean
sample standard deviation
sample size

(a) Confidence interval will be calculated using the formula:

For 98% confidence interval:

Pooled variance

So, the 98% confidence interval for the mean difference of the worm count in a lamb is

(b) The null and alternative hypothesis are:

; i.e. the true mean worm count in Drug-treated and Untreated sheep are not different.

; i.e., the true mean worm count in Drug-treated sheep is less than the Untreated sheep .

and the level of significance is given as

Test-statistic:   with

The test-statistic is calculated as

P-value:

Since it is a left-tailed hypothesis.

The p-value is calculated as

Decision:

Since,

So, at the data provide enough evidence to support the alternative hypothesis, i.e., .

Hence, "we conclude that the true mean count in the Drug-treated sheep is reduced."

(c) The assumptions to perform a hypothesis test for two independent sample t-test are:

• Selection has to be done through a SRS(Simple random sample)
• Individual observations are to be independent.
• Groups are to be independent.
• Sample size to be (>30) or the difference has to be normally distributed.