Question

We wonder if caffeine facilitates the learning of nonsense syllables. We randomly assign participants to one of two groups. People in the experimental group drink 2 cups of coffee and then learn a list of nonsense syllables. People in the control group drink 2 cups of plain water and then learn the same list. We record the number of trials required to perfectly learn the list for each participant. Did participants who drank the coffee learn the list faster than participants who drank the water? Be sure to interpret your answer completely, including a graph if appropriate.

Experimental Coffee	Control water
7	9
9	12
7	15
11	17
10	14

Answer 1

We are given the following data and are required to make the conclusion that the participants who drank coffee learn the list faster than participants who drank water.

Experimental(coffee) Control(Water)

7 9

9 12

7 15   

11 17

10 14

I suggest to solve this problem using z-test for two means since the sample size is greater than 30(One of the conditions to use large sample tests)

Here we have n1(coffee) = 44, n2(water)=67

Now we have to find

and

=>=8.8 and =13.4

Since are not known, we use s1 and s2 (sample standard deviations) to estimate

s1= and s2=

xi    yi      

7 -1.1 1.21 9 -4.4 19.36

9 0.2 0.04 12 -1.4 1.96

7 -1.1 1.21 15 1.6 2.56

11 2.2 4.84 17 3.6 12.96

10 1.2 1.44 14 0.6 0.36

Now we calculate s1()

=> s1 =

=0.20(0.196 actually)

=>s1=0.20

Now we calculate s2(  

=>s2 =

  

=0.56(0.563 actually)

=>s2 =0.56

Now that we have calculated s1 and s2, we now frame our null hypothesis and alternate hypothesis

Null hypothesis

i.e., the number of trials is equal

Alternate hypothesis

i.e., the number of trials are not equal(Two-tailed test)

Test statistic under

z=  /

=  

=-61.03

Conclusion

Since ,

we reject the null hypothesis

Hence participants who drank coffee learnt the list faster than those who drank water