Question

Both before and after seeing a movie designed to reduce sexism, five males responded to a symbolic sexism questionnaire. This questionaire measured covert sexist attitudes (moe subtle ones). The symbolic sexism questions were included in a large battery of personality questions that were completed one week before and after seeing the movie. Hence, it was unlikely that any participant would have guessed the researcher's hypothesis. High scores reflect greater sexism.

Before After

35     32

40     35

47     46

68     50

78     36

a. State the null hypothesis using symbols

b. Compute the appropriate test statistic, showing all of your computations.

c. For this analysis, the cutoff = + - 2.776. Can you reject the null hypothesis? Explain your response.

d. Draw the comparison (null) distribution and indicate values at 3 levels (data, t-values, probabilities).

e. Write out the statistic as if you were reporting this in a journal article.

f. Compute the 95% confidence interval. Hint: use the t values provided above.

Answer 1

Part a

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: There is no significant difference in average sexism score before and after seeing a movie.

Alternative hypothesis: H_a: The average sexism score after seeing a movie is reduced as compared to score after seeing a movie.

H₀: µ_D = 0

H_a: µ_D < 0

This is a lower tailed/left tailed/one tailed paired t-test.

Part b

Test statistic = t = (M_D - µ_D) / [S_D/sqrt(n)]

From given data, we have

M_D = 13.8

S_D = 17.1085

n = 5

df = n – 1 = 5 – 1 = 4

t = (13.8 – 0)/[17.1085/sqrt(5)]

t = 13.8/ 7.6511

t = 1.8037

Test statistic = 1.8037

Part c

We have t = 1.8037

Cutoff = ±2.776

So, test statistic lies between ±2.776.

So, we do not reject the null hypothesis.

Part d

We are given

n = 5

df = n – 1 = 5 – 1 = 4

t = 1.8037

so, by using t-table or excel, we have

P-value = 0.9272

P-value is greater than alpha 0.05.

Test statistic value is less than cut-off value 2.776.

Part e

The paired t-test (t=1.80, p = 0.9272) concludes that there is no significant difference in average sexism score before and after seeing a movie. There is insufficient evidence to conclude that the average sexism score after seeing a movie is reduced as compared to score after seeing a movie.