DIODGIO-UNAPCDA86101000000414d8c50080000&ck-m.1; Attempts: Average: /11 6. The t
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DIODGIO-UNAPCDA86101000000414d8c50080000&ck-m.1; Attempts: Average: /11 6. The t test for two independent samples - One-tailed example using tables A Aa Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because S4% of first marriages end in divorce, social scientists have begun investigating influences on marital satisfaction. [Data source: This data was obtained from National Center for Health Statistics.] Suppose a social psychologist sets out to look at the role of age of entering the marriage in relationship longevity. He decides to measure marital satisfaction in a group cf couples married after age 30 and a group of coupies married re age 30. He chooses the Marital Satisfaction Inventory, because it refers to "partner" and "relationship" rather than "spouse" and "marriage," which makes it useful for research with both traditional and nontraditional couples. Higher scores on the Marital Satisfaction Inventory indicate greater satisfaction. There is one score per couple. Assume that these scores are normally distributed and that the variances of the scores are the same among couples married after age 30 as among couples married before age 30. The psychologist thinks that couples married after age 30 will have greater relationship satisfaction than couples márried before age 30. He identifies the null and alternative hypotheses as: Ho : ?couples married after age 30- Hs: Hcouples maried after age 30 Hcouples mamed before age 30 Hcouples maried before age 30 This is a tailed test. The psychologist collects the data. A group of 51 couples married after age 30 scored an average of 45.8 with a sample standard deviation of 9 on the Marital Satisfaction Inventory. A group of 54 couples married before age 30 scored an average of 40.6 with a sample standard deviation of 8. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom. The degrees of freedom areExplanation / Answer
Solution:
Here, we have to use t-test for two independent samples. The null and alternative hypothesis for this test is given as below:
Null hypothesis: H0: The average relationship satisfaction score for the couples married after age 30 and before age 30 is same.
Alternative hypothesis: Ha: The average relationship satisfaction score for the couples married after age 30 is more than that of couples who married before age 30.
H0: µcouples married after age 30 = µcouples married before age 30
H0: µcouples married after age 30 > µcouples married before age 30
This is a one tailed test.
From given information, we are given
N1 = 51, X1bar = 45.8, S1 = 9
N2 = 54, X2bar = 40.6, S2 = 8
Level of significance = ? = 0.01
Assuming equal population variances, the degrees of freedom is given as below:
Degrees of freedom = N1 + N2 – 2 = 51 + 54 – 2 = 103
Critical value = Critical t-score = 2.3631
(By using t table or excel)
Now, we have to find pooled variance. Formula for pooled variance is given as below:
Sp2 = [(n1 – 1)*S1^2 + (n2 – 1)*S2^2]/(n1 + n2 – 2)
Sp2 = [(51 – 1)*9^2 + (54 – 1)*8^2]/(51 + 54 – 2)
Sp2 = 72.2524
Standard error = sqrt(Sp2*(1/N1 + 1/N2))
Standard error = sqrt(72.2524*(1/51 + 1/54))
Standard error = 1.6597
Difference in sample means = X1bar – X2bar = 45.8 – 40.6 = 5.2
Test statistic = t = (X1bar – X2bar) / sqrt[Sp2*((1/n1)+(1/n2))]
Test statistic = t = 5.2/1.6597
Test statistic = t = 3.1330
P-value = 0.0011
(by using t-table or excel)
P-value < alpha value
So, we reject the null hypothesis that the average relationship satisfaction score for the couples married after age 30 and before age 30 is same.
There is sufficient evidence to conclude that the average relationship satisfaction score for the couples married after age 30 is more than that of couples who married before age 30.
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