Question

This question set will use the following scenario that we saw on last week’s homework assignment: 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.

A. What is the dependent variable? [3 points]

B. Identify the sample. [3 points]

C. Have assumptions been met to conduct a single mean z test? Explain how you checked each assumption. [4 points]

D. Is this a one- or two-tailed test? Explain why.

Answer 1

Given that,
population mean(u)=100
standard deviation, σ =15
sample mean, x =105
number (n)=50
null, Ho: μ=100
alternate, H1: μ>100
level of significance, α = 0.05
from standard normal table,right tailed z α/2 =1.645
since our test is right-tailed
reject Ho, if zo > 1.645
we use test statistic (z) = x-u/(s.d/sqrt(n))
zo = 105-100/(15/sqrt(50)
zo = 2.357
| zo | = 2.357
critical value
the value of |z α| at los 5% is 1.645
we got |zo| =2.357 & | z α | = 1.645
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value : right tail - ha : ( p > 2.357 ) = 0.009
hence value of p0.05 > 0.009, here we reject Ho
ANSWERS
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a.
The dependent variable (sometimes known as the responding variable) is what is being studied and measured in the experiment.
It's what changes as a result of the changes to the independent variable. An example of a dependent variable is how tall you are at different ages.
b.
A psychologist has a dataset containing the WAIS-III scores from a random sample of 50 adults who are members of a specific organization.
c.
null, Ho: μ=100
alternate, H1: μ>100
d.
one tailed test
test statistic: 2.357
critical value: 1.645
decision: reject Ho
p-value: 0.009
we have enough evidence to support the claim that the mean WAIS-III score in the population of all members of this organization is greater than the known national mean of 100.