Asked by preet malhotra on May 18, 2024
Verified
In the past, the average age of employees of a large corporation has been 40 years.Recently, the company has been hiring older individuals.In order to determine whether there has been an increase in the average age of all the employees, a sample of 64 employees was selected.The average age in the sample was 45 years with a standard deviation of 16 years.Let α = .05.
a.
State the null and the alternative hypotheses.
b.
Compute the test statistic.
c.
Using the p-value approach, test to determine whether or not the mean age of all employees is significantly more than 40 years.
Null Hypothesis
A statement used in statistics that proposes there is no significant difference or effect, serving as the default assumption to be tested against an alternative hypothesis.
Test Statistic
A statistic (a function of the data) used in statistical hypothesis testing to decide whether to reject the null hypothesis.
P-value Approach
A method in hypothesis testing that uses the p-value, the probability of obtaining test results at least as extreme as the observed, under the assumption the null hypothesis is true.
- Comprehend the process involved in developing null and alternative hypotheses in hypothesis testing.
- Compute and elucidate the test statistic within the context of hypothesis evaluation.
- Ascertain the importance of test outcomes through the analysis of the p-value.
Verified Answer
a.
H0: μ
40 yearsHa: μ > 40 years
b.
t = 2.5
c.
p-value (.0075) is between .005 and .01; reject H0; the mean age of all employees is significantly more than 40 years.
Learning Objectives
- Comprehend the process involved in developing null and alternative hypotheses in hypothesis testing.
- Compute and elucidate the test statistic within the context of hypothesis evaluation.
- Ascertain the importance of test outcomes through the analysis of the p-value.
Related questions
A Random Sample of 25 Students Selected from the Student ...
A Random Sample of 100 People Was Taken ...
In Hypothesis Tests About a Population Proportion, P 0 Represents The ...
As a General Guideline, the Research Hypothesis Should Be Stated ...
If the Obtained Value Is Less Than the Critical Value,what ...