Question

A political scientist hypothesize that a political ad will increase attitudes about a particular issue. The scientist randomly asks 25 individuals walking by to see the ad and then take a quiz on the issue. The general public that knows little to nothing about the issue, on average, scores 50 on the quiz. The individuals that saw the ad scored an average of 47.55 with a variance of 28.73. What can the political scientist conclude with an α of 0.05?

a) What is the appropriate test statistic?
---Select--- na z-test one-sample t-test independent-samples t-test related-samples t-test

b)
Population:
---Select--- the ad individuals walking by general public the particular issue the political ad
Sample:
---Select--- the ad individuals walking by general public the particular issue the political ad

c) Compute the appropriate test statistic(s) to make a decision about H₀.
(Hint: Make sure to write down the null and alternative hypotheses to help solve the problem.)
critical value =  ; test statistic =
Decision:  ---Select--- Reject H0 Fail to reject H0

d) If appropriate, compute the CI. If not appropriate, input "na" for both spaces below.
[  ,  ]

e) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
d =  ;   ---Select--- na trivial effect small effect medium effect large effect
r² =  ;   ---Select--- na trivial effect small effect medium effect large effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly higher on the quiz than the general public.Individuals that watched the political ad scored significantly lower on the quiz than the general public.    Individuals that watched the political ad did not score significantly different on the quiz than the general public.

Answer 1

a) Appropriate test statistic : t-test independent-samples

b) Population: general public
Sample: individuals walking by

c) x̅ = 47.55, s² = 28.73, n = 25

α = 0.05

Null and Alternative hypothesis:

Ho : µ ≤ 50

H1 : µ > 50

Test statistic:

t = (x̅- µ)/√(s²/n) = (47.55 - 50)/√(28.73/25) = -2.2854

df = n-1 = 24

Critical value, t-crit = ABS(T.INV(0.05, 24)) = 1.711

Decision:

Fail to reject the null hypothesis

d) 95% Confidence interval :

At α = 0.05 and df = n-1 = 24, two tailed critical value, t-crit = T.INV.2T(0.05, 24) = 2.064

Lower Bound = x̅ - t-crit*√(s²/n) = 47.55 - 2.064 *√(28.73/25) = 45.3375

Upper Bound = x̅ + t-crit*√(s²/n) = 47.55 + 2.064 * √(28.73/25) = 49.7625

45.3375 < µ < 49.7625

e) Cohen's d = (x̅- µ)/s = -0.46 ; medium effect

r² = d²/(d²+4) = 0.0496 ; small effect

f) Make an interpretation based on the results.

Individuals that watched the political ad scored significantly lower on the quiz than the general public.