The average final exam score for the statistics course is 77%. A professor wants to see If average score for students who are given colored pens on the first day of class is different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96 What can be concluded at the the a=0.01 level of significince level of significance?

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The average final exam score for the statistics course is 77%. 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 different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.

70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96

What can be concluded at the α = 0.01 level of significance?

a. For this study, we should use [Select an answer]

b. The null and alternative hypotheses would be:

\[ H_0: \, ? \, \]

\[ H_1: \, ? \, \]

c. The test statistic = ______ (please show your answer to 3 decimal places.)

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

e. The p-value is [Select an answer]

f. Based on this, we should [Select an answer]

g. Thus, the final conclusion is that:

- ○ The data suggest the population mean is not significantly different from 77 at α = 0.01, 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 77.

- ○ The data suggest the population mean is significantly different from 77 at α = 0.01, 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 different from 77.

- ○ 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 different from 77 at α = 0.01, 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 different from 77.

Hint: 
Helpful Videos: Calculations [link], Setup [link], Interpretations [link]
Transcribed Image Text:The average final exam score for the statistics course is 77%. 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 different. The final exam scores for the 14 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal. 70, 65, 83, 90, 88, 69, 97, 100, 88, 79, 96, 83, 70, 96 What can be concluded at the α = 0.01 level of significance? a. For this study, we should use [Select an answer] b. The null and alternative hypotheses would be: \[ H_0: \, ? \, \] \[ H_1: \, ? \, \] c. The test statistic = ______ (please show your answer to 3 decimal places.) d. The p-value = ______ (Please show your answer to 4 decimal places.) e. The p-value is [Select an answer] f. Based on this, we should [Select an answer] g. Thus, the final conclusion is that: - ○ The data suggest the population mean is not significantly different from 77 at α = 0.01, 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 77. - ○ The data suggest the population mean is significantly different from 77 at α = 0.01, 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 different from 77. - ○ 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 different from 77 at α = 0.01, 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 different from 77. Hint: Helpful Videos: Calculations [link], Setup [link], Interpretations [link]
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