Suppose in one season, one baseball team averaged 20 run per game ( team 1), and team 2 averaged 10 runs . Assume each team had 10 hitters (n=10 for both). Assume that we don’t know the population standard deviations on each teams hits, but assume the sample standard deviations are 5 for each team. Test whether this difference is significant at the 95% confidence level, i.e., it is rarely likely to occur by chance if one team isn’t really better than the other. Use this information to answer questions 8 -12 below(Hint: Solve like “Are Men and Women Equal Talkers” Problems)The appropriate test statistic for testing whether the difference between these two means is unlikely to have happened by chance is the z-statisticb .t-statisticchi-square statisticF-statistic The value of the test statistic is (assume population standard deviations are unknown, and not equal). 14.14.401.6004.46 At the 95% confidence level, can we say this is a common difference in scores, given what we know about their standard deviations, or would this have been a rare event to have happened strictly by chance. CommonRareBorderlineRare for one team, common for the other The true population difference between these two teams’ scores is (with 95% probability) likely to be within what range (use 2 tail test)3.10 and 7.103.10 and 17.104.94 and 15.068 and 12 Suppose we had only one team with 10 hitters, that hit 20 runs per game after attending a special training camp, compared to the same players mean batting record of 10 runs the year before. (Matched Pairs). Assume the sample standard deviation of the before and after differences for this group of 10 hitters was 5. Assume the null hypothesis is that the true difference in the population is 0. Then the appropriate test statistic (z, t, F or chi-square) calculated from the difference after training would be 6.325 c. 2.12320.020 d. None of the above

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Answered: Suppose in one season, one baseball…

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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Suppose in one season, one baseball team averaged 20 run per game ( team 1), and team 2 averaged 10 runs . Assume each team had 10 hitters (n=10 for both). Assume that we don’t know the population standard deviations on each teams hits, but assume the sample standard deviations are 5 for each team. Test whether this difference is significant at the 95% confidence level, i.e., it is rarely likely to occur by chance if one team isn’t really better than the other. Use this information to answer questions 8 -12 below

(Hint: Solve like “Are Men and Women Equal Talkers” Problems)

The appropriate test statistic for testing whether the difference between these two means is unlikely to have happened by chance is the

z-statistic

b .t-statistic

chi-square statistic
F-statistic

The value of the test statistic is (assume population standard deviations are unknown, and not equal).

14.14
.401
.600
4.46

At the 95% confidence level, can we say this is a common difference in scores, given what we know about their standard deviations, or would this have been a rare event to have happened strictly by chance.

Common
Rare
Borderline
Rare for one team, common for the other

The true population difference between these two teams’ scores is (with 95% probability) likely to be within what range (use 2 tail test)
3.10 and 7.10
3.10 and 17.10
4.94 and 15.06
8 and 12

Suppose we had only one team with 10 hitters, that hit 20 runs per game after attending a special training camp, compared to the same players mean batting record of 10 runs the year before. (Matched Pairs). Assume the sample standard deviation of the before and after differences for this group of 10 hitters was 5. Assume the null hypothesis is that the true difference in the population is 0. Then the appropriate test statistic (z, t, F or chi-square) calculated from the difference after training would be

6.325 c. 2.123
20.020 d. None of the above

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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