Question

Scores on the Wechsler Adult Intelligence Scale- Third Edition (WAIS-III) are nationally standardized to be normally distributed with a mean of 100 and standard deviation of 15. A psychologist has a dataset containing the WAIS-III scores from a random sample of 50 adults who are members of a specific organization. They want to know if there is evidence that the mean WAIS-III score in the population of all members of this organization is greater than the known national mean of 100. In the sample of 50 adults, the observed sample mean was 105. When doing any hand calculations, show all work.

1) Our comparison distribution will be a distribution of sample means. What are the shape, mean, and standard deviation (i.e., standard error) of that distribution of sample means?

Answer 1

let X is WAIS-III score so X is normal with population mean=100 and population SD=SD=15

We have to test that WAIS-III score in given specific organisation is more than national average of 100

so

for this we have

sample size =n=50 sample mean =105

for testing purpose, we will use the distribution of sample means of the samples from the organization since population score is following normal distribution then the sample mean will also follow normal distribution hence

The shape will be bell-shaped.

mean of sample mean is given by

SD of the sample mean called as the standard error is given by

now test statistics is given by

since the test is right-tailed so

P-value=P(Z>2.36)=0.009

since P-value is low so we will reject H0 at 0.01,0.05 and upper level of significances hence we reject H0 that is there is statistically significant evidence to conclude that the population mean in the given specific organization is more than the national average of 100 .