Morgan City Fire Chief Sidney Pyro is concerned about the low efficiency scores that his firefighters receive at the state testing institute. Chief Pyro believes that these scores result because some firefighters are not in good physical condition. Pyro orders 75 randomly selected firefighters to participate in an hour of exercise per day. Another 200 firefighters have no required exercise. After 60 days, all firefighters are tested again by the state. Chief Pyro collects the data and performs a two-sample independent t-test by using SPSS to examine if there is a statistically significant difference between the treatment and control groups; the SPSS results are shown in the table below. GroupsNMeanStd. DeviationStd. Error MeanTest ScoresTreatment7574.531.43.6 Control20070.626.31.9Formulate a null and research hypothesis:H0:H1:Collect all the necessary data:Mean score of the treatment group:Mean score of the control group:Sample size of the treatment group:Sample size of the control group:Standard deviation of the treatment group:Standard deviation of the control group:Decide which test to use.Determine the level of significance. Levene's Test for Equality of Variancet-test for Equality of Means FSig.tdfSig.Mean DifferenceTest ScoresEqual variances assumed0.02480.67230.95822730.30473.9 Equal variances not assumed 0.9208257.230.30373.95. Based on the results of Levene’s test, find the proper t test statistic and the p-value.6. Compare the test statistic to the critical value, and compare the p-value to the alpha level (level of significance).7. Reject, or do not reject, the null hypothesis.8. What is your conclusion?

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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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Morgan City Fire Chief Sidney Pyro is concerned about the low efficiency scores that his firefighters receive at the state testing institute. Chief Pyro believes that these scores result because some firefighters are not in good physical condition. Pyro orders 75 randomly selected firefighters to participate in an hour of exercise per day. Another 200 firefighters have no required exercise. After 60 days, all firefighters are tested again by the state. Chief Pyro collects the data and performs a two-sample independent t-test by using SPSS to examine if there is a statistically significant difference between the treatment and control groups; the SPSS results are shown in the table below.

	Groups	N	Mean	Std. Deviation	Std. Error Mean
Test Scores	Treatment	75	74.5	31.4	3.6
	Control	200	70.6	26.3	1.9

Formulate a null and research hypothesis:
- H₀:
- H₁:
Collect all the necessary data:
- Mean score of the treatment group:
- Mean score of the control group:
- Sample size of the treatment group:
- Sample size of the control group:
- Standard deviation of the treatment group:
- Standard deviation of the control group:
Decide which test to use.
Determine the level of significance.

		Levene's Test for Equality of Variance	t-test for Equality of Means
		F	Sig.	t	df	Sig.	Mean Difference
Test Scores	Equal variances assumed	0.0248	0.6723	0.9582	273	0.3047	3.9
	Equal variances not assumed			0.9208	257.23	0.3037	3.9

5. Based on the results of Levene’s test, find the proper t test statistic and the p-value.

6. Compare the test statistic to the critical value, and compare the p-value to the alpha level (level of significance).

7. Reject, or do not reject, the null hypothesis.

8. What is your conclusion?

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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