Question

The t test for two independent samples - One-tailed example using tables

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 the National Center for Health Statistics.]

Suppose a clinical psychologist sets out to look at the role of intactness of family of origin in relationship longevity. He decides to measure marital satisfaction in a group of couples from divorced families and a group of couples from intact families. 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 from divorced families as among couples from intact families.

Q. The psychologist thinks that couples from divorced families will have less relationship satisfaction than couples from intact families. He identifies the null and alternative hypotheses as:

H₀: μcouples from divorced families couples from divorced families ( ) ?? μcouples from intact families couples from intact families

H₁: μcouples from divorced families couples from divorced families ( ) ?? μcouples from intact families couples from intact families

Q. This is a ( ) 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.

Q. The degrees of freedom are ( ) ?? .

Q. With α = 0.01, 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 (-2.423 -2.668 2.326 2.054) ?? .

Q. 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 (2.5308 89.3929 44.8423 91.0182 ) ?? Q. The estimated standard error of the difference in means is (2.5308 89.3929 91.0182 1.1934) ??   

Q. Calculate the t statistic. The t statistic is ( -1.50 -1.40 -1.70 -2.25) ??   

Q. The t statistic (does/does not) ??   lie in the critical region for a one-tailed hypothesis test. Therefore, the null hypothesis is (rejected/not rejected) ??

Q. The psychologist (can/can not)  ??   conclude that couples from divorced families have less relationship satisfaction than couples from intact families.

Answer 1

Please rate. cheers !!