Do left handed starting pitchers pitch the same number of innings per game on average as right handed starting pitchers? A researcher looked at eleven randomly selected left handed starting pitchers' games and eleven randomly selected right handed pitchers' games. The table below shows the results.Left: 5 6 7 7 5 6 6 8 6 7Right: 6 5 3 6 6 5 4 5 5 5Assume that both populations follow 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: (please enter a decimal) 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 ααBased on this, we should the null hypothesis.Thus, the final conclusion is that ...The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean innings per game for left handed starting pitchers is not the same as the population mean innings per game for right handed starting pitchers.The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean innings per game for left handed starting pitchers is equal to the population mean innings per game for right handed starting pitchers.The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the mean innings per game for the eleven left handed starting pitchers that were looked at is not the same as the mean innings per game for the eleven right handed starting pitchers that were looked at.The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean innings per game for left handed starting pitchers is not the same as the population mean innings per game for right handed starting pitchers.Interpret the p-value in the context of the study.If the sample mean innings per game for the 10 lefties is the same as the sample mean innings per game for the 10 righties and if another another 10 lefties and 10 righties are observed then there would be a 0.66% chance of concluding that the mean innings per game for the 10 lefties and the 10 righties differ by at least 1.3 innings per gameIf the population mean innings per game for left handed starting pitchers is the same as the population mean innings per game for right handed starting pitchers and if another 10 lefties and 10 righties are observed then there would be a 0.66% chance that the mean number of innings per game for the 10 lefties would differ by at least 1.3 innings from the mean innings per game for the 10 righties.There is a 0.66% chance that the mean innings per game for the 10 lefties differs by at least 1.3 innings per game compared to the 10 righties.There is a 0.66% chance of a Type I error.Interpret the level of significance in the context of the study.If the population mean innings per game for lefties is the same as the population mean innings per game for righties and if another 10 lefties and 10 righties are observed, then there would be a 10% chance that we would end up falsely concluding that the sample mean innings per game for these 10 lefties and 10 righties differ from each other.There is a 10% chance that your team will win whether the starting pitcher is a lefty or a righty. What you really need is better pitchers.There is a 10% chance that there is a difference in the population mean innings per game for lefties and righties.If the population mean innings per game for left handed starting pitchers is the same as the population mean innings per game for right handed starting pitchers and if another 10 lefties and 10 righties are observed then there would be a 10% chance that we would end up falsely concluding that the population mean innings per game for the lefties is not the same as the population mean innings per game for the righties

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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 left handed starting pitchers pitch the same number of innings per game on average as right handed starting pitchers? A researcher looked at eleven randomly selected left handed starting pitchers' games and eleven randomly selected right handed pitchers' games. The table below shows the results.

Left: 5 6 7 7 5 6 6 8 6 7

Right: 6 5 3 6 6 5 4 5 5 5

Assume that both populations follow 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: (please enter a decimal)

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 significant at αα = 0.10, so there is sufficient evidence to conclude that the population mean innings per game for left handed starting pitchers is not the same as the population mean innings per game for right handed starting pitchers.
- The results are statistically insignificant at αα = 0.10, so there is statistically significant evidence to conclude that the population mean innings per game for left handed starting pitchers is equal to the population mean innings per game for right handed starting pitchers.
- The results are statistically significant at αα = 0.10, so there is sufficient evidence to conclude that the mean innings per game for the eleven left handed starting pitchers that were looked at is not the same as the mean innings per game for the eleven right handed starting pitchers that were looked at.
- The results are statistically insignificant at αα = 0.10, so there is insufficient evidence to conclude that the population mean innings per game for left handed starting pitchers is not the same as the population mean innings per game for right handed starting pitchers.
Interpret the p-value in the context of the study.
- If the sample mean innings per game for the 10 lefties is the same as the sample mean innings per game for the 10 righties and if another another 10 lefties and 10 righties are observed then there would be a 0.66% chance of concluding that the mean innings per game for the 10 lefties and the 10 righties differ by at least 1.3 innings per game
- If the population mean innings per game for left handed starting pitchers is the same as the population mean innings per game for right handed starting pitchers and if another 10 lefties and 10 righties are observed then there would be a 0.66% chance that the mean number of innings per game for the 10 lefties would differ by at least 1.3 innings from the mean innings per game for the 10 righties.
- There is a 0.66% chance that the mean innings per game for the 10 lefties differs by at least 1.3 innings per game compared to the 10 righties.
- There is a 0.66% chance of a Type I error.
Interpret the level of significance in the context of the study.
- If the population mean innings per game for lefties is the same as the population mean innings per game for righties and if another 10 lefties and 10 righties are observed, then there would be a 10% chance that we would end up falsely concluding that the sample mean innings per game for these 10 lefties and 10 righties differ from each other.
- There is a 10% chance that your team will win whether the starting pitcher is a lefty or a righty. What you really need is better pitchers.
- There is a 10% chance that there is a difference in the population mean innings per game for lefties and righties.
- If the population mean innings per game for left handed starting pitchers is the same as the population mean innings per game for right handed starting pitchers and if another 10 lefties and 10 righties are observed then there would be a 10% chance that we would end up falsely concluding that the population mean innings per game for the lefties is not the same as the population mean innings per game for the righties

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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