Question

The average final exam score for the statistics course is 74%. 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 lower. The final exam scores for the 12 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.

79, 60, 52, 72, 67, 47, 54, 79, 61, 80, 80, 47

What can be concluded at the the αα = 0.10 level of significance level of significance?

For this study, we should use Select an answer t-test for a population mean z-test for a population proportion

The null and alternative hypotheses would be:

H0:H0:  ? p μ  Select an answer ≠ > = <       

H1:H1:  ? μ p  Select an answer ≠ > = <    

The test statistic ? t z  =  (please show your answer to 3 decimal places.)

The p-value =  (Please show your answer to 4 decimal places.)

The p-value is ? > ≤  αα

Based on this, we should Select an answer accept reject fail to reject  the null hypothesis.

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 lower than 74 at αα = 0.10, 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 lower than 74.

The data suggest the population mean is not significantly lower than 74 at αα = 0.10, 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 74.

The data suggest the populaton mean is significantly lower than 74 at αα = 0.10, 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 lower than 74.

Answer 1

The statistical software output for this problem is :

H₀ : μ = 74
H_A : μ < 74

Test statistics = -2.433

P-value = 0.0166

The p-value is ≤  αα

Reject  the null hypothesis.

The data suggest the population mean is significantly lower than 74 at αα = 0.10, 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 lower than 74.