Question

The average final exam score for the statistics course is 76%. A professor wants to see if the average final exam score for students who are given colored pens on the first day of class is higher. The final exam scores for the 16 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.

86, 97, 69, 93, 85, 88, 99, 67, 91, 85, 73, 66, 100, 90, 71, 82

What can be concluded at the the αα = 0.05 level of significance level of significance?

1. For this study, we should use Select an answer z-test for a population proportion t-test for a population mean
2. The null and alternative hypotheses would be:

H0:H0:  ? μ p  ? > = < ≠       

H1:H1:  ? p μ  ? < = ≠ >    

3. The test statistic ? z t  =  (please show your answer to 3 decimal places.)
4. The p-value =  (Please show your answer to 4 decimal places.)
5. The p-value is ? > ≤  αα
6. Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean final exam score for students who are given colored pens at the beginning of class is not significantly higher than 76 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is higher than 76.
   • The data suggest the populaton mean is significantly higher than 76 at αα = 0.05, so there is statistically significant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is higher than 76.
   • The data suggest the population mean is not significantly higher than 76 at αα = 0.05, so there is statistically insignificant evidence to conclude that the population mean final exam score for students who are given colored pens at the beginning of class is equal to 76.

Answer 1