Question

A team of behavioral neuroscientists wants to know whether Froot Loops or Cheerios are more rewarding for rats. Under laboratory conditions, it is trivial to train rats that they will receive a reward if they press a lever. These neuroscientists assign 15 rats to receive a Froot Loop when they press a lever and another 15 rats to receive a Cheerio when they press a lever. Over a 24-hour period, rats in the Froot Loops condition pressed the lever an average of 195.46 times with a variance of 418.63. Over the same 24-hour period, rats in the Cheerios condition pressed the lever an average of 165.88 times with a variance of 901.13.

A. What is μ? If it is not reported, answer “N/A”. B. What is σ? If it is not provided, answer “N/A”.

C. What sample means are provided? If this is a within-subjects design, include D̄ as well as x̄.

D. What are the s values? If this is a within-subjects design, report s for each condition as well as sD.

E. What is N? If this is a between-subjects design, report n1 and n2 in addition to N.

F. What are the degrees of freedom?
G. Is this a one- or two-tailed test?
H. What is the null hypothesis (H0)?
I. What is the alternative hypothesis (Ha)?
J. What inferential test should be used here? (Note that the options are a z test, a one-sample t test, an independent-samples t test, or a related- samples t test.)

K. What is the standard error? Depending on what kind of inferential test is being used, this will be σx̄, sx̄, sx̄1−x̄2, or sD̄.

L. What is zcrit or tcrit? (Obviously, this depends on whether this question calls for a z or t test.)

M. What is your obtained test statistic (i.e., what is zobt or tobt)?

N. Given the obtained and critical values, what is the appropriate con- clusion to draw?

Answer 1

A.

N/A (No population means are given)

B.

N/A (No population standard deviations are given)

C.

Sample means are

= 195.46

= 165.88

This is not a within-subjects design because different rats were assigned in different treatments.

D.

s values are,

s₁ = = 20.46045

s₁ = = 30.01883

E.

N = 15 + 15 = 30

n1 = 15

n2 = 15

F.

degrees of freedom for independent sample is,

DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

DF = (418.63/15 + 901.13/15)² / { [ (418.63 / 15)² / (15 - 1) ] + [ (901.13 / 15)² / (15 - 1) ] }

= 25 (Rounding to nearest integer)

G.

We are testing for whether Froot Loops or Cheerios are more rewarding for rats. So, this is a two-tailed test.

H.

I.

J.

Since we do not know the population standard deviations and the samples are independent, we would use independent-samples t test.

K.

sx̄1−x̄2 = sqrt[ (s₁²/n₁) + (s₂²/n₂) ]

= sqrt[ (418.63/15) + (901.13/15) ]

= 9.379979

L.

tcrit for DF = 25 and 5% significance level is 2.06

M.

tobt = ( - ) / sx̄1−x̄2

= (195.46 - 165.88) / 9.379979

= 3.15

N.

Since tobt > tcrit, we reject null hypothesis H0 and conclude there is significant evidence that  Froot Loops or Cheerios are more rewarding for rats.