Statistical Analysis Results For Indigo Insurance Company Employees Survey

Question 1 – Independent-samples t-test

There are 1,343 employees with less than 5 years tenure and 2,995 with more than 5 years or more. The mean scale of engagement with the supervisor of employees with less than 5 years is 14.16. Consequently, the mean scale of engagement with the supervisors of employees with 5 years or more is 13.59.

The Levene’s p > 0.05, thus we do not reject the null of Levene’s test and conclude that the variance in the level of engagement with the supervisors of the employees with less than 5 years is not significantly different than that of employees with 5 years or more.

Using assumed equal variances, the p-value <0.05. Thus, we choose to reject the null hypothesis and conclude that the mean level of engagement with the supervisor for employees with less than 5 years and the employees with 5 or more years is significantly different.

There are 2,290 female employees and 2,048 male employees. The mean level of engagement with the supervisor of female employees is 13.8. Consequently, the mean level of engagement with the supervisors of male employees is 13.73.

The Levene’s p < 0.05, thus we reject the null of Levene’s test and conclude that the variance in the level of engagement with the supervisors of the female employees is significantly different than that of male employees.

Using the equal variances not assume, the p >0.05. Thus, we choose to not reject the null hypothesis and conclude that the mean level of engagement with the supervisor for female employees and the male employees with 5 or more years is not significantly different.

The mean level of engagement with the team is 11.75 with a standard deviation of 6.09 while the mean of the level of engagement with the supervisor is 13.77 with a standard deviation of 5.11. The number of participants in each condition is 4,338. 

The significant value (2-tailed) is 0.000.Since the p < 0.05, we choose to reject the null hypothesis and conclude that there is a significant statistical difference between the mean level of engagement with the team and the level of engagement with the supervisor. From the paired samples statistics, we can conclude that the level of engagement with the supervisor was significantly more than the level of engagement with the team

1. What is the population we can draw conclusions about in this study?

The population is 20 staff employed by Indigo Insurance Company.

1. What does the highlighted section of the distribution in Figure 1 represent?

The highlighted section is the probability of getting between 50 and 50.4 work-related emails.

The random sample of 20 employees of Indigo Insurance Company taken by the employee advocacy group turned out to have a mean of 50.8 work-related emails to respond to in that week. Does this sample look like it belongs to the sampling distribution displayed in Figure 1? Justify your answer.

No, it does not. The mean of 50.8 work-related emails is more than the maximum expected mean of 50.4 work-related emails.

Given the sample was randomly selected and that the number of work-related emails each employee was required to respond to was recorded accurately, what conclusion can we reach from part (c)?

Since the mean of 50.8 work-related emails is beyond the confidence interval of 50 to 50.4 work-related emails, thus we are not confident about the mean of work-related emails Indigo Insurance Company employees.