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.60, 88, 80, 82, 93, 87, 62, 77, 90, 67, 75, 73, 55What 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:  ? μ p  ? < ≠ > =        H1:H1:  ? μ p  ? > ≠ < =    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 ? > ≤  ααBased on this, we should Select an answer fail to reject accept reject  the null hypothesis.Thus, the final conclusion is that ...The data suggest the populaton mean is significantly different from 81 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 different from 81.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 81 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 different from 81.The data suggest the population mean is not significantly different from 81 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 81.

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Asked Nov 18, 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.

60, 88, 80, 82, 93, 87, 62, 77, 90, 67, 75, 73, 55

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

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

 H0:H0:  ? μ p  ? < ≠ > =       

 H1:H1:  ? μ p  ? > ≠ < =    

  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.)
  3. The p-value is ? > ≤  αα
  4. Based on this, we should Select an answer fail to reject accept reject  the null hypothesis.
  5. Thus, the final conclusion is that ...
    • The data suggest the populaton mean is significantly different from 81 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 different from 81.
    • 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 81 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 different from 81.
    • The data suggest the population mean is not significantly different from 81 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 81.
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Expert Answer

Step 1

1) The t-test :

Here, the sample size is small and sample standard deviation is unknown. Therefore, t-test for population mean is appropriate in this case.

Step 2

2) Calculation of test statistic:

The hypotheses to be tested are:

H0: μ = 81, that is, the population mean is 81.

Versus:

H0: μ ≠ 81, that is, population mean is different from 81.

Step 3

Calculation of test statistic:

Here, the population standard deviation, σ, is unknown; it is estimated by the sample standard deviation as, s = 12.2029(using the Excel function ‘=STDEV (A1:A1...

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t = Vn 76.0769 81 12.2029 V13 1.455

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