Question

Researchers from the University of Kent, UK, were interested in whether collectivist or individualist attitudes are related to one’s intent to comply with social distancing and safety guidelines during COVID-19. Participants were classified as either collectivist or individualist and rated their intent to comply with guidelines on a scale from 1-5, where 1 is definitely not and 5 is definitely yes. Please conduct an independent-groups t-test to determine if there is a significant difference in intention to comply between individualists and collectivists.

In addition, please:
- report cohen’s d
- report r^2
- conduct and interpret an F-MAX test
- include 95% confidence intervals
- report your answer in words that directly address the research question
- and show all work in step by step detail.

Collective

x f

3 2

4 6

5 12

Individual

x f

1 1

2 3

3 11

4 13

5 2

Answer 1

we will apply independent samples t-test.

Collective	Individual
x	f	x	f
3	2	1	1
4	6	2	3
5	12	3	11
		4	13
		5	2

or

S.No.	Collective	Individual
1	3	1
2	3	2
3	4	2
4	4	2
5	4	3
6	4	3
7	4	3
8	4	3
9	5	3
10	5	3
11	5	3
12	5	3
13	5	3
14	5	3
15	5	3
16	5	4
17	5	4
18	5	4
19	5	4
20	5	4
21		4
22		4
23		4
24		4
25		4
26		4
27		4
28		4
29		5
30		5
N	20	30
Mean=	4.5	4.258064516

The provided sample means are shown below:

Xˉ1​=4.5 and Xˉ2​=4.26

Also, the provided sample standard deviations are:

s1​=0.69 and s2​=0.89

and the sample sizes are n1​=20 and n2​=30.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:μ1​ = μ2​

Ha: μ1​ ≠ μ2​

This corresponds to a two-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is \alpha = 0.05α=0.05, and the degrees of freedom are df = 48. In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this two-tailed test is tc​=2.011, for α=0.05 and df=48.

The rejection region for this two-tailed test is R={t:∣t∣>2.011}.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

t = 1.018

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=1.018≤tc​=2.011, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.3138, and since p=0.3138≥0.05, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1​ is different than μ2​, at the 0.05 significance level.

Two groups are not significantly different or collectivist or individualist attitudes are not related to one’s intent to comply with social distancing and safety guidelines during COVID-19.

Confidence Interval

The 95% confidence interval is −0.234<μ1​−μ2​<0.714.

Graphically

Cohen's D

Cohen's d = (4.26 - 4.5) ⁄ 0.796304 = 0.301392.

report r^2

The sample size needs to be equal for that
conduct and interpret an F-MAX test

F_RATIO = s²_MAX / s²_MIN

F_RATIO = 0.792/0.4761

F_RATIO = 1.66

df = 29

and F critical = 2.11

As, F ratio is not greater than 2.11, we fail to reject Ho or the variances of two groups "Collective" and "Indiciduak" are not significantly different.

Include 95% confidence intervals

The 95% confidence interval is −0.234<μ1​−μ2​<0.714.

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