Question

Standardized measures seem to indicate that the average level of anxiety has increased over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was u = 15.1. A sample of n = 16 of today’s children produces a mean score of M = 23.3 with SS = 240. (a) Based on the sample, has there been a significant change in the average level of anxiety since the 1950s? Use a two-tailed test with alpha = .01. List, number, state, and clearly show all 4 steps of the hypothesis test. For step 2, state alpha and describe the critical regions of the test statistic distribution. Step 4 must also answer the question posed in the problem. Clearly show all calculations steps to get answers including formulas needed to solve this problem.

Answer 1

H₀: = 15.1

H₁: 15.1

s =

= = 4

The test statistic t = ()/(s/)

                             = (23.3 - 15.1)/(4/)

                             = 8.2

At alpha = 0.01, the critical values are t^* = +/- 2.947

Reject H₀, if t < -2.947 or, t > 2.947

Since the test statistic value is greater than the positive critical value (8.2 > 2.947), so we should reject the null hypothesis.

So at 0.01 significance level, we can conclude that there has been a change in the average level of anxiety since the 1950s.