Are the means for the final exams different for all statistics class delivery types? The table below shows the scores on final exams from several randomly selected classes that used the different delivery types.OnlineHybridFace-to-Face71837984737978848481818280 86 79 81Assume that all distributions are normal, the three population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.Part (a)State the null hypothesis.H0: ?online = ?hybrid = ?face to face.H0: At least two of the group means ?online, ?hybrid, ?face to face are not equal. Part (b)State the alternative hypothesis.Ha: ?online = ?hybrid = ?face to face.Ha: At least two of the group means ?online, ?hybrid, ?face to face are not equal. Part (c)Enter an exact number as an integer, fraction, or decimal.df(num) = Part (d)Enter an exact number as an integer, fraction, or decimal.df(denom) = Part (e)State the distribution to use for the test.F13, 15F2, 13 F2, 15F13, 2F15, 13Part (f)What is the test statistic? (Round your answer to two decimal places.)Part (g)What is the p-value? (Round your answer to four decimal places.)Part (h)Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. Part (i)Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write appropriate conclusions.(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)? = (ii) Decision:reject the null hypothesisdo not reject the null hypothesis (iii) Reason for decision:Since ? < p-value, we reject the null hypothesis.Since ? < p-value, we do not reject the null hypothesis. Since ? > p-value, we do not reject the null hypothesis.Since ? > p-value, we reject the null hypothesis.(iv) Conclusion:There is sufficient evidence to support that the mean scores of the different class delivery types are different.There is not sufficient evidence to support that the mean scores of the different class delivery types are different.

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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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Are the means for the final exams different for all statistics class delivery types? The table below shows the scores on final exams from several randomly selected classes that used the different delivery types.

Online	Hybrid	Face-to-Face
71	83	79
84	73	79
78	84	84
81	81	82
80		86
		79
		81

Assume that all distributions are normal, the three population standard deviations are approximately the same, and the data were collected independently and randomly. Use a level of significance of 0.05.

Part (a)

State the null hypothesis.
H₀: ?_online = ?_hybrid = ?_{face to face}

.H₀: At least two of the group means ?_online, ?_hybrid, ?_{face to face} are not equal.
Part (b)

State the alternative hypothesis.
H_a: ?_online = ?_hybrid = ?_{face to face}.

H_a: At least two of the group means ?_online, ?_hybrid, ?_{face to face} are not equal.
Part (c)

Enter an exact number as an integer, fraction, or decimal.
df(num) =
Part (d)

Enter an exact number as an integer, fraction, or decimal.
df(denom) =
Part (e)

State the distribution to use for the test.
F_13,

₁₅F_{2, 13}

F_{2, 15}

F_{13, 2}

F_{15, 13}
Part (f)

What is the test statistic? (Round your answer to two decimal places.)
Part (g)

What is the p-value? (Round your answer to four decimal places.)
Part (h)

Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value.
Part (i)

Indicate the correct decision ("reject" or "do not reject" the null hypothesis) and write appropriate conclusions.
(i) Alpha (Enter an exact number as an integer, fraction, or decimal.)
? =

(ii) Decision:
reject the null hypothesisdo not reject the null hypothesis

(iii) Reason for decision:
Since ? < p-value, we reject the null hypothesis.

Since ? < p-value, we do not reject the null hypothesis.

Since ? > p-value, we do not reject the null hypothesis.

Since ? > p-value, we reject the null hypothesis.

(iv) Conclusion:
There is sufficient evidence to support that the mean scores of the different class delivery types are different.

There is not sufficient evidence to support that the mean scores of the different class delivery types are different.

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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