Do left handed starting pitchers pitch the same number of innings per game on average as right handed starting pitchers? A researcher looked at nine randomly selected left handed starting pitchers' games and ten randomly selected right handed pitchers' games. The table below shows the results.Left: 6 4 5 5 7 5 5 6Right: 5 3 6 4 3 7 6 7 4Assume that both populations follow a normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance?For this study, we should use Select an answer z-test for a population proportion t-test for the difference between two independent population means t-test for a population mean z-test for the difference between two population proportions t-test for the difference between two dependent population means The null and alternative hypotheses would be: H0:H0: Select an answer μ1 p1 Select an answer > < = ≠ Select an answer p2 μ2 (please enter a decimal) H1:H1: Select an answer μ1 p1 Select an answer > = < ≠ Select an answer μ2 p2 (Please enter a decimal)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 accept reject fail to reject the null hypothesis.Thus, the final conclusion is that ...The results are statistically significant at αα = 0.05, 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 = 0.05, 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.The results are statistically insignificant at αα = 0.05, 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 = 0.05, so there is sufficient evidence to conclude that the mean innings per game for the nine left handed starting pitchers that were looked at is not the same as the mean innings per game for the ten right handed starting pitchers that were looked at.Interpret the p-value in the context of the study.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 8 lefties and 9 righties are observed then there would be a 55.48% chance that the mean number of innings per game for the 8 lefties would differ by at least 0.4 innings from the mean innings per game for the 9 righties.If the sample mean innings per game for the 8 lefties is the same as the sample mean innings per game for the 9 righties and if another another 8 lefties and 9 righties are observed then there would be a 55.48% chance of concluding that the mean innings per game for the 8 lefties and the 9 righties differ by at least 0.4 innings per gameThere is a 55.48% chance of a Type I error.There is a 55.48% chance that the mean innings per game for the 8 lefties differs by at least 0.4 innings per game compared to the 9 righties.Interpret the level of significance in the context of the study.There is a 5% 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 8 lefties and 9 righties are observed then there would be a 5% 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 rightiesIf the population mean innings per game for lefties is the same as the population mean innings per game for righties and if another 8 lefties and 9 righties are observed, then there would be a 5% chance that we would end up falsely concluding that the sample mean innings per game for these 8 lefties and 9 righties differ from each other.There is a 5% chance that your team will win whether the starting pitcher is a lefty or a righty. What you really need is better pitchers.

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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 nine randomly selected left handed starting pitchers' games and ten randomly selected right handed pitchers' games. The table below shows the results.

Left: 6 4 5 5 7 5 5 6

Right: 5 3 6 4 3 7 6 7 4

Assume that both populations follow a normal distribution. What can be concluded at the the αα = 0.05 level of significance level of significance?

For this study, we should use Select an answer z-test for a population proportion t-test for the difference between two independent population means t-test for a population mean z-test for the difference between two population proportions t-test for the difference between two dependent population means

The null and alternative hypotheses would be:

H0:H0: Select an answer μ1 p1 Select an answer > < = ≠ Select an answer p2 μ2 (please enter a decimal)

H1:H1: Select an answer μ1 p1 Select an answer > = < ≠ Select an answer μ2 p2 (Please enter a decimal)

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 ? ≤ > αα
Based on this, we should Select an answer accept reject fail to reject the null hypothesis.
Thus, the final conclusion is that ...
- The results are statistically significant at αα = 0.05, 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 = 0.05, 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.
- The results are statistically insignificant at αα = 0.05, 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 = 0.05, so there is sufficient evidence to conclude that the mean innings per game for the nine left handed starting pitchers that were looked at is not the same as the mean innings per game for the ten right handed starting pitchers that were looked at.
Interpret the p-value in the context of the study.
- 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 8 lefties and 9 righties are observed then there would be a 55.48% chance that the mean number of innings per game for the 8 lefties would differ by at least 0.4 innings from the mean innings per game for the 9 righties.
- If the sample mean innings per game for the 8 lefties is the same as the sample mean innings per game for the 9 righties and if another another 8 lefties and 9 righties are observed then there would be a 55.48% chance of concluding that the mean innings per game for the 8 lefties and the 9 righties differ by at least 0.4 innings per game
- There is a 55.48% chance of a Type I error.
- There is a 55.48% chance that the mean innings per game for the 8 lefties differs by at least 0.4 innings per game compared to the 9 righties.
Interpret the level of significance in the context of the study.
- There is a 5% 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 8 lefties and 9 righties are observed then there would be a 5% 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
- If the population mean innings per game for lefties is the same as the population mean innings per game for righties and if another 8 lefties and 9 righties are observed, then there would be a 5% chance that we would end up falsely concluding that the sample mean innings per game for these 8 lefties and 9 righties differ from each other.
- There is a 5% chance that your team will win whether the starting pitcher is a lefty or a righty. What you really need is better pitchers.

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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