The revenue Commissioners Ireland conducted a contest for promotion. The ages of the unsuccessful applicants are given below. Some of the applicants who were unsuccessful in getting a promotion charged that the competition involved discrimination based on age. treat the data as samples from larger populations and use a 0.05 significance level to test the claim that the mean age of the successful applicants. Based on the result, does there appear to be descrimination based on age?
ages of unsuccessful applicants
34,37,37,38,41,42,43,44,44,45,45,45,46,48,49,53,53,54,54,55,56,57,60
ages of successful applicants
27,33,36,37,38,38,39,42,42,43,43,44,44,44,45,45,45,45,46,46,47,47,48,48,49,49,51,51,52,54
1.state the obviouse claim (what is alleged?)
2.what happens if the claim is false?
3.what is the null and alternative hypothesis?
4.will this be a Z or T distribution?
5.what is the test statistics (statdisk)
6.What is the conclusion?
To analyze the data and answer the questions, we will perform a hypothesis test. Here are the steps to follow:
1. State the obvious claim: The claim is that the competition involved discrimination based on age, implying that there is a significant difference in the mean age between successful and unsuccessful applicants.
2. What happens if the claim is false? If the claim is false, then there is no discrimination based on age, and any difference in mean age between the two groups is due to chance or random variation.
3. Define the null and alternative hypotheses:
- Null hypothesis (H0): The mean age of successful applicants is the same as the mean age of unsuccessful applicants.
- Alternative hypothesis (Ha): The mean age of successful applicants is significantly different from the mean age of unsuccessful applicants.
4. Determine whether a Z or T distribution should be used:
Since we do not have information about the population standard deviation, we will use a T distribution for this hypothesis test. This is because we are using sample data to make inferences about the entire population.
5. Calculate the test statistics:
To calculate the test statistics, we can use statistical software like Statdisk. Once you input the data for both groups, specify that it should perform an independent samples T-test using a 0.05 significance level. The software will provide the test statistics, including the T-value and the p-value.
6. Draw a conclusion:
Based on the p-value obtained from the T-test, we will compare it to the significance level (0.05) to determine whether there is enough evidence to reject the null hypothesis. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is evidence of discrimination based on age. If the p-value is greater than or equal to 0.05, we fail to reject the null hypothesis and conclude that there is no evidence of discrimination based on age.
You can use a statistical software package or spreadsheet program (e.g., Excel) to calculate the T-test and obtain the p-value, which will allow you to draw a conclusion based on the results.