A researcher wants to know if there is a difference in how busy someone is based on whether that person identifies as an early bird or a night owl. The researcher gathers data from people in each group, coding the data so thathigher scores represent higher levels of being busy, and tests for a difference between the two at the .05 level of significance.Early BirdNight Owl2326281027203319262630182212252526

The given data is: Early BirdNight Owl2326281027203319262630182212252526The objective is to tests for a difference between the two at the 0.05 level of significance. Le us denote:= population mean of busy scores for early birds.= population mean of busy scores for night owls. For Early Bird:The sample mean is:The sample standard deviation is:For Night Owl:The sample mean is:The sample standard deviation is:The hypothesis under consideration is:This is two-tailed test. We can use two sample t-test to compare two groups.The test statistic is given as:Plugging the values, we get: The value of test statistic is 2.9277. To determine if the difference is statistically significant, we compare the calculated t-value at the 0.05 level of significance , with degrees of freedom calculated as:The critical value is given as:The t-critical value is 2.13145. To find the critical value we use the following excel function:"=T.INV.2T(0.05,15)"The screenshot is as follows:Since, we reject null hypothesis at 5% level of significance and conclude that, based on given data, we have sufficient evidence that there is a statistically significant difference in how busy someone is based on whether they identify as a early bird or a night owl. Reason:If , we fail to reject null hypothesis at given level of significance, else we reject it. There is a statistically significant difference in how busy someone is based on whether they identify as a early bird or a night owl.