thank you very much. 6. The t test for two independent samples One-tailed exampl
ID: 2934191 • Letter: T
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thank you very much.
6. The t test for two independent samples One-tailed example using tables Aa Most engaged couples expect or at least hope that they will have high levels of marital satisfaction. However, because 54% 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 counseling psychologist sets out to look at the role of intactness of family of origin in relationship longevity. She decides to measure marital satisfaction in a group of couples from divorced families and a group of couples from intact families. She 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 from divorced families as among couples from intact families The psychologist thinks that couples from divorced families will have less relationship satisfaction than couples from intact families. She identifies the null and alternative hypotheses as: Ho Hcouples from divorced families H1· Haouples from divorced families- Hcouples from intact families couples from intact families This isa tailed test. The psychologist collects the data. A group of 30 couples from divorced families scored an average of 21.5 with a sample standard deviation of 10 on the Marital Satisfaction Inventory. A group of 27 couples from intact families scored an average of 25.8 with a sample standard deviation of 9. Use the t distribution table. To use the table, you will first need to calculate the degrees of freedom The degrees of freedom are To see the table, click on the arrow and then on the words "The t distribution" that appear in the space below. with = .01, the critical t-score (the value for a t-score that separates the tail from the main body of the distribution, forming the critical region) is the critical values for both surrounding df values and select the larger t value to use as your critical t-score. If you fail to reject the null hypothesis, you can later check the smaller t value to decide whether to interpolate. However for the purposes of this problem, you can just assume that if your t statistic is not more extreme than the larger t value, you will not reject the null hypothesis. Also,the table includes only positive t values. Since the t distribution is symmetrical, for a one-tailed test where the alternative hypothesis is less than, simply negate the t value provided in the table.]) . (Note: If your df value is not included in this table, look up To calculate the t statistic, you first need to calculate the estimated standard error of the difference in means. To calculate this estimated standard error, you first need to calculate the pooled variance. The pooled variance is . The estimated standard error of the difference in means is (Hint: For the most precise results, retain four decimal places from your calculation of the pooled variance to calculate the standard error.) Calculate the t statistic. Thet statistic is (Hint: For the most precise results, retain four decimal places from your previous calculation to calculate the t statistic.) The t statistic lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is The psychologist conclude that couples from divorced families have less relationship satisfaction than couples from intact families.Explanation / Answer
Given that,
mean(x)=21.5
standard deviation , s.d1=10
number(n1)=30
y(mean)=25.8
standard deviation, s.d2 =9
number(n2)=27
null, Ho: u1 = u2
alternate, H1: u1 < u2
level of significance, = 0.01
from standard normal table,left tailed t /2 =2.479
since our test is left-tailed
reject Ho, if to < -2.479
we use test statistic (t) = (x-y)/sqrt(s.d1^2/n1)+(s.d2^2/n2)
to =21.5-25.8/sqrt((100/30)+(81/27))
to =-1.709
| to | =1.709
critical value
the value of |t | with min (n1-1, n2-1) i.e 26 d.f is 2.479
we got |to| = 1.70865 & | t | = 2.479
make decision
hence value of |to | < | t | and here we do not reject Ho
p-value:left tail - Ha : ( p < -1.7086 ) = 0.04971
hence value of p0.01 < 0.04971,here we do not reject Ho
ANSWERS
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null, Ho: u(couples from diverced families) = u(couples from intact families)
alternate, H1: u(couples from diverced families) < u(couples from intact families)
This is a one tailed
df = 26
test statistic: -1.709
critical value: -2.479
decision: do not reject Ho
p-value: 0.04971
we don't have evidence that couples from diverced families have less rellationship satisfaction than couples from intact families.
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