Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, XXXXXXXXXXIn the 1950s, the average score on the Child Manifest Anxiety...

Standardized measures seem to indicate that the average level of anxiety has increased gradually over the past 50 years (Twenge, 2000). In the 1950s, the average score on the Child Manifest Anxiety Scale was μ = 15.1. A sample of
n
= 16 of today’s children produces a mean score of
x̅
= 23.3 with

s²
= 16. Based on this sample (and using a two-tailed test with α = .01), has there been a significant change in the average level of anxiety since the 1950s?

The calculated statistics for this research study are as follows:

With
df
= 15, the critical values are
t
= ±2.947. For these data, the sample variance is
s²

= 16, the estimated standard error is
s_M

= 1, and
t
= 8.20; Cohen’s
d
= 2.05.

1. a) Using a two-tailed test with α = .01, draw an appropriate conclusion about the null hypothesis and whether or not there has been a significant change in the level of anxiety over the past 50 years.

b) Write a sentence that demonstrates the outcome of the hypothesis test, and the effect size, would appear in a research report. (Put more simply, write a sentence spelling out the conclusions drawn about the research question, based on this sample, and include the relevant statistics –
df, calculatedt-statistic,
p-value, and effect size.)