There is a theory that people who drink caffeine can run longer than those who d

Question

There is a theory that people who drink caffeine can run longer than those who do not. To test this theory a random sample of seven people who drink caffeine and a random sample of seven people who do not drink caffeine was obtained and their length of time they could run non-stop was measured, in seconds. a. At the 5% significance level, can you conclude that those who drink caffeine can run longer than those who do not? b. Are the samples independent or dependent? C. If independent, would using dependent samples have been better? Why or Why not? If dependent explain why dependent samples were used.

Explanation / Answer

We can use two sample t test to test the hypothesis.

Ho: Those who drink caffeine and who do not run equal.

against H1: Those who drink caffeine can run longer than those who do not.

mean(x) = 231.714

mean(y)= 438.714

mean(xy) = 58898.58

s2x= 5073.238 , s2y = 1419.905

1

Sp2= ----------------------- [ (m-1) s2x + (n-1)s2y]

m + n -2

Sp = 56.98

t test is

(mean x - mean y) - 0 (here we consider population mean is equal, so value is 0)

--------------------------------- ~ t12

Sp [SQRT(1/m +1/n)]

-207

------------------ = - 6.796

30.46

This value is not liyng in the 5% significant level.

So we have sufficient evidence to reject Ho.

That is we can conclude that Those who drink caffeine can run longer than those who do not.

b)

Independent samples are measurements made on two different sets of items.

So this is independent sample.

C) If dependent samples are used then chenge in value of one variable results in change in value of other variable.

Here Data of one variable is sufficiently unrelated than data counted for other variable.

So using independent samples are better.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.