Question

**JUDGING OFF THE FOLLOWING QUESTION...I DONT THINK IT IS
THE SAME GROUP OF PEOPLE TWICE. THE MAIN GROUP IS SPLIT INTO TWO -
SO ARE WE SURE IT WOULD BE PAIRED?**

In the main study, researchers collected 80 adults. Adults were randomly divided into 2 groups, 40 each. First group was given cheerios for a month and the second group was given toasted oats for a month. Average ldl cholesterol were 4.64 mmol/l in cheerios group and 4.00 mmol/l in toasted oats group. the sample standard deviations were 0.72 mmol/l and 1.15 mmol/l in oat bran group. Your task is to perform a hypothesis test with 0.05 significance level.

A.) So, do we use

**- two sample t-test**

Data: cheerios and ToastedOats

t=3.002, df = 78, p-value = 0.003602

Alternative hypothesis: true difference in means is not equal to 0.

**- welch two sample-test**

Data: Cheerios and ToastedOats

t=3.002, df = 65.353, p-value = 0.003797

Alternative hypothesis: true difference in means is not equal to 0

**- paired t-test**

Data: Cheerios and ToastedOats

t=3.075, df = 39, p-value = 0.003835

Alternative hypothesis: true difference in means is not equal to 0.

Using software output you choose, write a valid conclusion in paragraph format. Make sure to include descriptions about the mean difference with units, statistical significance. Include both statistical and medical conclusion in your statement as if you were reporting in a journal article.

Answer #1

It is not paired for sure because there are two different groups, each of 40 people. So, it is clear that there is no paired data, but we have two different groups.

If we assume population with equal variance, then two sample t test is appropriate test to be used in this case.

So, select first test

**two sample t-test**

**Data: cheerios and ToastedOats**

**t=3.002, df = 78, p-value =
0.003602**

**Alternative hypothesis: true difference in means is
not equal to 0.**

Mean difference between two groups is 0.64 mmol/l. Result is significant at 0.05 significance level because the p value corresponding to the test statistics is 0.0036, which is less than significance level of 0.05. So, rejecting the null hypothesis and concluding that there a significant difference between means of two groups.

Medical conclusion:-Average ldl cholesterol are different between cheerios group and toasted oats group

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