The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 17 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.(a)Develop the null and alternative hypotheses most appropriate for this situation.H0: ? < 17Ha: ? ≥ 17H0: ? = 17Ha: ? ≠ 17 H0: ? > 17Ha: ? ≤ 17H0: ? ≤ 17Ha: ? > 17H0: ? ≥ 17Ha: ? < 17(b)Comment on the conclusion whenH0cannot be rejected.We can conclude that there is statistical evidence that the new bonus plan increases the mean monthly sales volume.We can conclude that there is not statistical evidence that the new bonus plan increases the mean monthly sales volume. (c)Comment on the conclusion whenH0can be rejected.We can conclude that there is statistical evidence that the new bonus plan increases the mean monthly sales volume.We can conclude that there is not statistical evidence that the new bonus plan increases the mean monthly sales volume.

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Description: The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 17 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan i

Given , Mean sale volume is 17 automobiles per month.

Answered: Develop the null and alternative…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.6: Summarizing Categorical Data

Problem 30PPS

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The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 17 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a one-month period.

(a)

Develop the null and alternative hypotheses most appropriate for this situation.

H₀: ? < 17

H_a: ? ≥ 17

H₀: ? = 17

H_a: ? ≠ 17

H₀: ? > 17

H_a: ? ≤ 17

H₀: ? ≤ 17

H_a: ? > 17

H₀: ? ≥ 17

H_a: ? < 17

(b)

Comment on the conclusion when

H₀

cannot be rejected.

We can conclude that there is statistical evidence that the new bonus plan increases the mean monthly sales volume.We can conclude that there is not statistical evidence that the new bonus plan increases the mean monthly sales volume.

(c)

Comment on the conclusion when

H₀

can be rejected.

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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