Reference no: EM132178445

1. A manager, who works for your company, said at a business meeting:

We have asked employees who would volunteer to participate in the survey. We paid $100 to each employee for the participation, to be fair and compensate for the time spent answering the survey questions. Because of this, the participation was high and we could achieve the sample size of 130. Based on this sample, we found that the confidence interval for the proportion of happy employees in our company is [97.6%, 99.2%], with the confidence level of 95%. Please note that we had to use the Student's t-distribution with 95 degrees of freedom to find this confidence interval. 

Thus, our analysis has shown that at least 97.6% of our company's employees are very happy. 

What is wrong with the manager's statement? Keep in mind that this question allows multiple correct answers and incorrect answers will result in the mark reduction. 

The sample which the manager used was biased and therefore it could not be used for the statistical analysis.

Not mentioning other errors, the manager used the incorrect number of degrees of freedom. 

Even if the manager had computed the confidence interval correctly, the manager failed to draw the correct conclusion. The mentioned confidence interval does not mean that at least 97.6% of employees are happy. 

The sample size must have been bigger, because one cannot compute the confidence intervals with sample sizes with fewer than 150 items. 

The manager must have used 99% confidence level. 

The manager used an incorrect probability distribution to find the confidence interval.