Question

A political scientist is interested in the effectiveness of a political ad about a particular issue. The scientist randomly asks 18 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 49.61 with a standard deviation of 5.02. What can the political scientist conclude with an α of 0.01?

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

Given

Sample size=n=18

Sample mean=m=49.61

Sample Standard deviation=S=5.02

a)

As we have to test population mean is equal to 50 or not for that we have taken a sample of 18 people also n<30 as well as we don't know about the population standard deviation hence we will use : one sample T test

b)

Since population is defined as group of objects on which our experiment (study) is intended In this case our study focus on the average score of the general public in the test so

Population:
the political ad general public the

Sample is defined as a part of population taken to estimate the population behavior hence in this case our sample is 18 peoples hence

Sample:individuals walking by the ad

c)

We need to test

Since we are using T statistics hence DF=n-1=18-1=17

Level of significance =0.01

And test is two tailed then critical value is given by

Crtical value =|2.898|

We reject H0 if t statistics >|2.898|

Where

P(t >critical value )=0.005 (half of level of significance)

Now test statistics is given by

=-0.33

Since -.33 less than critical value hence we failed to reject the Null hypothesis.

d)

99% (I.e. (1-0.01)*100%) confidence interval is given by

So interval is

(46.181,53.039)