Question

[6 marks]

A researcher was interested in finding out whether Moral Reasoning could be enhanced if students were taught using Moral Dilemmas. Subjects were given a Moral Reasoning Test before the treatment (using moral dilemmas) and after the treatment and the results are shown in Table 1 below.

Table 1 : Mean Moral Reasoning Score Before and After Teaching Using Moral Dilemmas
	N	Mean	Std. Deviation	Std. Error Mean
Pretest	30	18.50	5.33	0.97
Posttest	30	23.86	4.75	0.87

1. Describe the findings in Table 1
2. State the null hypothesis
3. State the alternative hypothesis
4. Why is the paired t-test used? [as shown in Table 2 above]
5. What can you conclude from Table 2?

Table 2 : Paired t Test
	Mean	Std. Deviation	Std. Error Mean	Lower	Upper	t	df	Sig. (2 tailed)
Pretest	-5.36	2.90	0.62	-6.65	-4.08	-8.66	29	.000
Posttest

Answer 1

Solution :

a) The sample mean of the Moral reasoning test score before treatment is 18.50 with sample standard deviation 5.33. The standard error of the sample mean is 0.97.

The sample mean of the Moral reasoning test score after treatment is 23.86 with sample standard deviation 4.75. The standard error of the sample mean is 0.87.

b) The null hypothesis is as follows :

H​​​​​​0 : The population mean of the test scores before and after the treatment are same.

c) The alternative hypothesis is as follows :

H​​​​​​1 : The population mean of the test scores before treatment is less than the population mean of the test scores after the treatment.

d) Sice, the Moral reasoning test has been assigned to same 30 students, before and after the treatment, therefore this is a dependent sample and that's why paired t-test should be used.

e) The paired t-test is used. The test statistic is given by,

t = mean of pairs differences / Standard error

t = -5.36/0.62

t = -8.645

The value of the test statistic is -8.645.

The p-value given in the table-2 is 0.000.

In our question significance level is not given, Generally significance level of 0.01 or 0.05 is used. We shall use significance level of 0.01.

Significance level = 0.01

(0.000 < 0.01)

Since, p-value is less than the significance level of 0.01, therefore we shall reject the null hypothesis at 0.01 significance level.

Conclusion : At 0.01 significance level, there is sufficient evidence to conclude that Moral Reasoning could be enhanced if students were taught using Moral Dilemmas.