Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below. Playing Vs. Watching Sports Play 7 4 6 6 7 6 3 10 3 3 Watch 5 1 6 6 3 6 1 10 2 2 Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance? For this study, we should use The null and alternative hypotheses would be: H0:H0: (please enter a decimal) H1:H1: (Please enter a decimal) 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 results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports. The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average. The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports.

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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Do college students enjoy playing sports more than watching sports? A researcher randomly selected ten college students and asked them to rate playing sports and watching sports on a scale from 1 to 10 with 1 meaning they have no interest and 10 meaning they absolutely love it. The results of the study are shown below.

Playing Vs. Watching Sports

Play	7	4	6	6	7	6	3	10	3	3
Watch	5	1	6	6	3	6	1	10	2	2

Assume a Normal distribution. What can be concluded at the the αα = 0.10 level of significance level of significance?

For this study, we should use

The null and alternative hypotheses would be:

H0:H0: (please enter a decimal)

H1:H1: (Please enter a decimal)

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 results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean rating for playing sports is greater than the population mean rating for watching sports.
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the ten students that were surveyed rated playing sports higher than watching sports on average.
- The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean rating for playing sports is equal to the population mean rating for watching sports.

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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