# The average final exam score for the statistics course is 81%. 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 13 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.65, 78, 57, 77, 89, 62, 75, 63, 68, 86, 57, 76, 72What can be concluded at the α = 0.05 level of significance level of The test statistic ? t z   =    (please show your answer to 3 decimal places.)The p-value =     (Please show your answer to 4 decimal places.)significance?

Question
Asked Nov 19, 2019
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The average final exam score for the statistics course is 81%. 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 13 randomly selected students who were given the colored pens are shown below. Assume that the distribution of the population is normal.

65, 78, 57, 77, 89, 62, 75, 63, 68, 86, 57, 76, 72

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

1. The test statistic ? t z   =    (please show your answer to 3 decimal places.)
2. The p-value =     (Please show your answer to 4 decimal places.)

significance?

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## Expert Answer

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Step 1

Introduction:

The null and alternative hypotheses are as follows:

H0: μ = 81, vs. H1: μ ≠ 81.

When the population standard deviation is unknown and the sample standard deviation must be used in a test to determine whether the true population mean is equal to a given constant, then the t-test must be used.

The test statistic is of the form:

...

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