The t test for two independent samples - One-tailedexample using tables
Most engaged couples expect or at least hope that they will havehigh levels of marital satisfaction. However, because 54% of firstmarriages end in divorce, social scientists have beguninvestigating influences on marital satisfaction. [Data source:This data was obtained from the National Center for HealthStatistics.]
Suppose a clinical psychologist sets out to look at the role ofintactness of family of origin in relationship longevity. Hedecides to measure marital satisfaction in a group of couples fromdivorced families and a group of couples from intact families. Hechooses 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 andnontraditional couples. Higher scores on the Marital SatisfactionInventory indicate greater satisfaction. There is one score percouple. Assume that these scores are normally distributed and thatthe variances of the scores are the same among couples fromdivorced families as among couples from intact families.
Q. The psychologist thinks thatcouples from divorced families will have less relationshipsatisfaction than couples from intact families. He identifies thenull and alternative hypotheses as:
H?: ?couples from divorced families couples from divorcedfamilies ( ) ?? ?couples from intact familiescouples from intact families
H?: ?couples from divorced families couples from divorcedfamilies ( ) ?? ?couples from intact familiescouples from intact families
Q. This is a ( ) tailed test??
The Psychologist collects the data. A group of 30 couples fromdivorced families scored an average of 21.5 with a sample standarddeviation of 10 on the Marital Satisfaction Inventory. A group of27 couples from intact families scored an average of 25.8 with asample standard deviation of 9. Use the t distribution table. Touse the table, you will first need to calculate the degrees offreedom.
Q. The degrees of freedom are ( )?? .
Q. With ? = 0.01, the critical t-score (thevalue for a t-score that separates the tail from the main body ofthe distribution, forming the critical region) is (-2.423-2.668 2.326 2.054) ?? .
Q. To calculate the t statistic, you first needto calculate the estimated standard error of the difference inmeans. To calculate this estimated standard error, you first needto calculate the pooled variance. The pooled variance is(2.5308 89.3929 44.8423 91.0182 ) ?? Q. Theestimated standard error of the difference in means is(2.5308 89.3929 91.0182 1.1934) ??
Q. Calculate the t statistic. The t statisticis ( -1.50 -1.40 -1.70 -2.25) ??
Q. The t statistic (does/does not) ?? lie in the critical region for a one-tailed hypothesistest. Therefore, the null hypothesis is (rejected/notrejected) ??
Q. The psychologist (can/can not) ?? conclude that couples from divorced families have lessrelationship satisfaction than couples from intact families.
