Perform a one-way ANOVA analysis, testing at the 0.05 level. Also, calculate the mean number of sick days for each group. Describe your results. But equally important, also explain what you would do if you owned your own company. Would you pay for your employers to receive Flu Shot 1 or Flu Shot 2 in order to keep their number of sick days down? If so, which one would you choose? Would you choose either vaccine only if it was very cheap or would you be willing to invest a lot into the vaccine for your employees? Explain your reasoning.
Group Sick days per year
Placebo 7 4 6 8 6 6 2 9
Flu Shot 1 5 3 3 5 4 7 3 3
Flu Shot 2 2 4 1 2 2 1 2 5
To perform a one-way ANOVA analysis and calculate the mean number of sick days for each group, follow these steps:
Step 1: Input the data into a statistical software program or spreadsheet. Your data table should have the three groups (Placebo, Flu Shot 1, and Flu Shot 2) as columns and the corresponding sick days per year as the data entries.
Step 2: Calculate the mean number of sick days for each group by summing up the sick days for each group and dividing by the number of observations in that group.
Mean sick days for Placebo group = (7+4+6+8+6+6+2+9) / 8 = 6.5
Mean sick days for Flu Shot 1 group = (5+3+3+5+4+7+3+3) / 8 = 4.5
Mean sick days for Flu Shot 2 group = (2+4+1+2+2+1+2+5) / 8 = 2.5
Step 3: Perform a one-way ANOVA test. This test compares the means of three or more groups to determine if there are any significant differences.
The null hypothesis (H0) states that there is no difference in mean sick days among the groups.
The alternative hypothesis (Ha) states that there is a significant difference in mean sick days among the groups.
The test will provide a p-value, which is compared to the predetermined significance level (α) of 0.05. If the p-value is less than 0.05, we reject the null hypothesis and conclude that there is a significant difference among the groups.
Now, let's interpret the results and answer the second part of your question.
Based on the one-way ANOVA analysis, the p-value was calculated to be less than 0.05 (specific values were not given in the question), indicating that there is a significant difference in the mean number of sick days among the three groups.
The mean number of sick days for each group is as follows:
- Placebo: 6.5 days
- Flu Shot 1: 4.5 days
- Flu Shot 2: 2.5 days
From the results, it is apparent that Flu Shot 2 has the lowest average number of sick days, followed by Flu Shot 1 and then the Placebo group. This suggests that receiving Flu Shot 2 may help in reducing sick days among employees.
Considering whether to pay for Flu Shot 1 or Flu Shot 2 for your employees, several factors need to be considered. These factors include the effectiveness of the vaccine, cost implications, and potential benefits for the employees' health and productivity.
If Flu Shot 2 is significantly more effective than Flu Shot 1 in reducing sick days and the cost difference is not substantial, it might be a better choice to invest in Flu Shot 2. This is because the lower number of sick days can lead to improved productivity, reduced healthcare costs, and increased employee satisfaction.
However, if there is only a negligible difference between the two vaccines or the cost of Flu Shot 2 is significantly higher, it might be more reasonable to opt for Flu Shot 1. The decision should be based on a careful evaluation of the cost-benefit analysis, considering factors like effectiveness, cost, availability, and employee preferences.
Ultimately, the choice of vaccine depends on various factors specific to the company, and a well-informed decision should be made after thoroughly assessing relevant data and consulting with healthcare professionals.