Question

TWO MEANS – INDEPENDENT SAMPLES

Choose a variable from the advising.sav data set to compare group means. While the choice of which variable to test is up to you, you must remember that it must be a metric variable. The grouping variable, which is used to define the two groups to be compared, must be categorical.   You can look in the “Measure” column of the “Variable View” in the data file for help in determining which is which. The managerial question is whether or not there is a significant difference between the groups for the metric variable you have chosen.

Once you have the results, report your findings using the five step hypothesis testing procedure outlined in class. (See below.)   For Step 4, simply cut and paste the SPSS output into the report. This can be done by clicking on the desired portion of the output which will then be highlighted, and then right clicking on the highlighted portion and copying it to your flash drive. (Note that you may want to drop the results into a word document immediately since if you do not have SPSS on your personal laptop, you will not be able to open any SPSS output.) Then state the answer to the managerial question that was initially posed. For example, is there a significant difference between the two groups defined by the grouping variable (which you must identify in your report) for the metric variable tested? Also, interpret the confidence interval provided for the test. Does it indicate a significant difference or not?   

PAIRED SAMPLE T-TEST

Choose a pair of metric variables and run a paired sample t-test on the pair. Again, these must be metric variables. The managerial question will be “Is there a significant difference between the two variables?” for the pair. Report your findings using the same procedure described above, including an interpretation of the confidence interval.

REPORT(SAMPLE)

Your report will consist of two hypotheses tests, (one for the independent sample test and one for the paired sample test). It will look something like this (for the independent sample test):

1: H₀: μ₁= μ₂

H_a: μ₁ ≠ μ₂

2: Two group independent sample t-test (note that SPSS does everything as a t-test regardless of sample size).

3: α=.05 → t_crit = ±whatever the appropriate value is

4

Group Statistics
	status	N	Mean	Std. Deviation	Std. Error Mean
dotest	0	185	1494.071	2249.4948	165.3861
	1	50	803.280	1080.0304	152.7394

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
dotest	Equal variances assumed	13.465	.000	2.104	233	.036	690.7914	328.2585	44.0572	1337.5255
	Equal variances not assumed			3.068	169.287	.003	690.7914	225.1264	246.3747	1135.2080

5: Make a decision regarding the null hypothesis and interpret the confidence interval.

6: Answer the managerial question.

RESULTS AFTER RUNNING

INDEPENDENT

Group Statistics
	Gender	N	Mean	Std. Deviation	Std. Error Mean
OverallSatisfaction	Female	131	4.97	1.771	.155
	Male	145	4.99	1.488	.124

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
OverallSatisfaction	Equal variances assumed	5.905	.016	-.120	274	.904	-.024	.196	-.410	.363
	Equal variances not assumed			-.119	255.054	.905	-.024	.198	-.414	.366

PAIRED

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	DesiredConvenience	6.20	273	1.175	.071
	ActualConvenience	4.55	273	1.636	.099

Paired Samples Correlations
		N	Correlation	Sig.
Pair 1	DesiredConvenience & ActualConvenience	273	.213	.000

Paired Samples Test
		Paired Differences					t	df	Sig. (2-tailed)
		Mean	Std. Deviation	Std. Error Mean	95% Confidence Interval of the Difference
					Lower	Upper
Pair 1	DesiredConvenience - ActualConvenience	1.648	1.799	.109	1.434	1.863	15.140	272	.000

 

Answer 1

SOLUTION-

Before interpreted you must have to know this information which is given below

Step(1)

DEFINE

Hypotheses-

The null hypothesis (H₀) and alternative hypothesis (H₁) of the Independent Samples t Test can be expressed in two different but equivalent ways:

H₀: µ₁ = µ₂ ("the two population means are equal")
H₁: µ₁ ≠ µ₂ ("the two population means are not equal")

OR

H₀: µ₁ - µ₂ = 0 ("the difference between the two population means is equal to 0")
H₁: µ₁ - µ₂ ≠ 0 ("the difference between the two population means is not 0")

Levene’s Test for Equality of Variances -Recall that the Independent Samples t Test requires the assumption of homogeneity of variance -- i.e., both groups have the same variance. SPSS conveniently includes a test for the homogeneity of variance, called Levene's Test, whenever you run an independent samples T test.

The hypotheses for Levene’s test are:

H₀: σ₁² - σ₂² = 0 ("the population variances of group 1 and 2 are equal")
H₁: σ₁² - σ₂² ≠ 0 ("the population variances of group 1 and 2 are not equal")

This implies that if we reject the null hypothesis of Levene's Test, it suggests that the variances of the two groups are not equal; i.e., that the homogeneity of variances assumption is violated.

• The output in the Independent Samples Test table includes two rows: Equal variances assumed and Equal variances not assumed. If Levene’s test indicates that the variances are equal across the two groups (i.e., p-value large), you will rely on the first row of output, Equal variances assumed, when you look at the results for the actual Independent Samples t Test (under t-test for Equality of Means). If Levene’s test indicates that the variances are not equal across the two groups (i.e., p-value small), you will need to rely on the second row of output, Equal variances not assumed, when you look at the results of the Independent Samples t Test (under the heading t-test for Equality of Means).

Data Set-Up - Your data should include two variables (represented in columns) that will be used in the analysis. The independent variable should be categorical and include exactly two groups. (Note that SPSS restricts categorical indicators to numeric or short string values only.) The dependent variable should be continuous (i.e., interval or ratio).

Step(2)- OUTPUT

Group Statistics
	status	N	Mean	Std. Deviation	Std. Error Mean
dotest	0	185	1494.071	2249.4948	165.3861
	1	50	803.280	1080.0304	152.7394

The first section, Group Statistics, provides basic information about the group comparisons, including the sample size (n), mean, standard deviation, and standard error by group.

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
dotest	Equal variances assumed	13.465	.000	2.104	233	.036	690.7914	328.2585	44.0572	1337.5255
	Equal variances not assumed			3.068	169.287	.003	690.7914	225.1264	246.3747	1135.2080

The second section, Independent Samples Test, displays the results most relevant to the Independent Samples t Test. There are two parts that provide different pieces of information: (A) Levene’s Test for Equality of Variances and (B) t-test for Equality of Means.

Levene's Test for Equality of of Variances: This section has the test results for Levene's Test. From left to right:

• F is the test statistic of Levene's test
• Sig. is the p-value corresponding to this test statistic.

The p-value of Levene's test is printed as ".000" (but should be read as p < 0.001 -- i.e., p very small), so we we reject the null of Levene's test and conclude that the variance of groups is significantly different than that of other group. This tells us that we should look at the "Equal variances not assumed" row for the t test (and corresponding confidence interval) results. (If this test result had not been significant -- that is, if we had observed p > α -- then we would have used the "Equal variances assumed" output.)

t-test for Equality of Means provides the results for the actual Independent Samples t Test. From left to right:

note that mean difference is calculated by subtracting the mean of the second group from the mean of the first group. The associated p value is printed as "0.003"; double-clicking on the p-value will reveal the un-rounded number. SPSS rounds p-values to three decimal places, so any p-value too small as 0.003

Confidence Interval of the Difference: This part of the t-test output complements the significance test results. Typically, if the CI for the mean difference contains 0, the results are not significant at the chosen significance level. In this example, the 95% CI is [246.37, 1135.20, which does not contain zero; this agrees with the small p-value of the significance test.

Step(3)-

DECISION AND CONCLUSIONS-

Since p < .05 is less than our chosen significance level α = 0.05, we can reject the null hypothesis, and conclude that the that the groups are significantly different to each other.

Based on the results, we can state the following:

• There was a significant difference in mean mile time between non-athletes and athletes (t169.287 = 3.068, p < .05).
• The average of one group is 690.7914 more than the other group.

Ans(6): Answer the managerial question.

INDEPENDENT

Group Statistics
	Gender	N	Mean	Std. Deviation	Std. Error Mean
OverallSatisfaction	Female	131	4.97	1.771	.155
	Male	145	4.99	1.488	.124

Independent Samples Test
		Levene's Test for Equality of Variances		t-test for Equality of Means
		F	Sig.	t	df	Sig. (2-tailed)	Mean Difference	Std. Error Difference	95% Confidence Interval of the Difference
									Lower	Upper
OverallSatisfaction	Equal variances assumed	5.905	.016	-.120	274	.904	-.024	.196	-.410	.363
	Equal variances not assumed			-.119	255.054	.905	-.024	.198	-.414	.366

Conclusion-   same as previous steps .

Note-

P-VALUE -

• A small p-value (typically ≤ 0.05) indicates strong evidence against the null hypothesis, so you reject the null hypothesis.

• A large p-value (> 0.05) indicates weak evidence against the null hypothesis, so you fail to reject the null hypothesis.

• p-values very close to the cutoff (0.05) are considered to be marginal (could go either way). Always report the p-value so your readers can draw their own conclusions.

Answer 2