The average final exam score for the statistics course is 75%. 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. 87, 51, 68, 49, 75, 52, 58, 79, 84, 64, 59, 88 What can be concluded at the the αα = 0.01 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: H1:H1: The test statistic = (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 the null hypothesis. Thus, the final conclusion is that ... The data suggest the population mean is not significantly lower than 75 at αα = 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 75. 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 75 at αα = 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 lower than 75. The data suggest the populaton mean is significantly lower than 75 at αα = 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 lower than 75.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The average final exam score for the statistics course is 75%. 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.

87, 51, 68, 49, 75, 52, 58, 79, 84, 64, 59, 88

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

For this study, we should use
The null and alternative hypotheses would be:

H0:H0:

H1:H1:

The test statistic = (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 the null hypothesis.
Thus, the final conclusion is that ...
- The data suggest the population mean is not significantly lower than 75 at αα = 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 75.
- 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 75 at αα = 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 lower than 75.
- The data suggest the populaton mean is significantly lower than 75 at αα = 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 lower than 75.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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