Question

The average test score for the statistics course is 74%. A professor wants to see if the average test score for students who are given colored pens on the first day of class is higher. The test 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.

81, 61, 86, 63, 74, 91, 62, 70, 80, 94, 70, 87

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

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

H0: μ or p? ≠ > < =?   

H1: p or μ? < ≠ = >?

3. The test statistic? t or z  = ____ (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? > or ≤  α
6. Based on this, we should: fail to reject, reject, or accept the null hypothesis?
7. Thus, the final conclusion is that ...
   • The data suggest that the population mean test score for students who are given colored pens at the beginning of class is not significantly higher than 74 at α = 0.05, so there is statistically insignificant evidence to conclude that the population mean test score for students who are given colored pens at the beginning of class is higher than 74.
   • The data suggest the population mean is not significantly higher than 74 at α = 0.05, so there is statistically insignificant evidence to conclude that the population mean test 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 higher than 74 at α = 0.05, so there is statistically significant evidence to conclude that the population mean test score for students who are given colored pens at the beginning of class is higher than 74.

Answer 1