Question

Strack, Martin, and Stepper (1988) reported that people rate cartoons as funnier when holding a pen in their teeth (which forced them to smile) than when holding a pen in their lips (which forced them to frown). A researcher attempted to replicate this result using a sample of n = 25 adults between the ages 40 and 45. For each person, the researcher recorded the difference between the rating obtained while smiling and the rating obtained by frowning. On average, the cartoons were rated funnier when the participants were smiling, with an average difference of M D = 1.6 with SS = 150.In this problem, you do not have to calculate SS or the mean difference which is already provided. Do the data indicate that the cartoons are rated significantly funnier when the participants are smiling? Use a one-tailed test with α = .05

Need to find:

n = 25

df =

M_D= 1.6

μ_{D =}

s²=

S_{M D=}

1. State the hypothesis s and select alpha (consider one tailed or two tailed)

Sate hypothesis in words:

            Null stated in words:

            Alternative stated in words:

State hypothesis in symbols: Hₒ:

State alternative in symbols: H ₁:

2. Locate critical region for stated alpha:

3. Compute test statistic (Repeated measure t-score)

            Variance for D scores: S²

                        Estimated standard error S_MD :

                        Computed repeated measure t statistic:

4. Make a decision about the null hypothesis and state a conclusion.

  Decision:

Answer 1

n = 25

df = 25-1 = 24

MD= 1.6

μD = 1.6

s2= 150/24 = 6.25

SM D= sqrt(6.25/25) = 0.5

1. State the hypothesis s and select alpha (consider one tailed or two tailed)

Sate hypothesis in words: is the cartoons are rated significantly funnier when the participants are smiling

            Null stated in words: the cartoons are rated not significantly funnier when the participants are smiling

            Alternative stated in words: the cartoons are rated significantly funnier when the participants are smiling

State hypothesis in symbols: Hₒ:

State alternative in symbols: H 1:

2. Locate critical region for stated alpha:

3. Compute test statistic (Repeated measure t-score)

            Variance for D scores: S2 = 6.25

                        Estimated standard error SMD : 0.5

                        Computed repeated measure t statistic:

                                                

4. Make a decision about the null hypothesis and state a conclusion.

   Critical t:        1.7109

   Decision: Since t-value > Critical t:1.7109 ; so we reject H0

Thus we conlcude that the cartoons are rated significantly funnier when the participants are smiling