The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At α=0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 11.9 7.6 12.4 6.5 5.4 10.1 12.2 8.1 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ<10.0 Ha: μ≥10.0 B. H0: μ≥10.0 Ha: μ<10.0 C. H0: μ>10.0 Ha: μ≤10.0 D. H0: μ=10.0 Ha: μ≠10.0 E. H0: μ≠10.0 Ha: μ=10.0 F. H0: μ≤10.0 Ha: μ>10.0 (b) Use technology to find the P-value. P=nothing (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? A. Reject H0 because the P-value is greater than the significance level. B. Fail to reject H0 because the P-value is less than the significance level. C. Reject H0 because the P-value is less than the significance level. D. Fail to reject H0 because the P-value is greater than the significance level. (d) Interpret the decision in the context of the original claim. A. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is 10.0. B. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is greater than 10.0. C. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is 10.0. D. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is less than 10.0.

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 10.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At α=0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 11.9 7.6 12.4 6.5 5.4 10.1 12.2 8.1 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ<10.0 Ha: μ≥10.0 B. H0: μ≥10.0 Ha: μ<10.0 C. H0: μ>10.0 Ha: μ≤10.0 D. H0: μ=10.0 Ha: μ≠10.0 E. H0: μ≠10.0 Ha: μ=10.0 F. H0: μ≤10.0 Ha: μ>10.0 (b) Use technology to find the P-value. P=nothing (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null hypothesis. Which of the following is correct? A. Reject H0 because the P-value is greater than the significance level. B. Fail to reject H0 because the P-value is less than the significance level. C. Reject H0 because the P-value is less than the significance level. D. Fail to reject H0 because the P-value is greater than the significance level. (d) Interpret the decision in the context of the original claim. A. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is 10.0. B. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is greater than 10.0. C. At the 1% level of significance, there is sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is 10.0. D. At the 1% level of significance, there is not sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is less than 10.0.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Question

The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is

10.0.

As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At

α=0.01,

can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

11.9

7.6

12.4

6.5

5.4

10.1

12.2

8.1

(a) Write the claim mathematically and identify

and

Ha.

Which of the following correctly states

and

Ha?

H0:

μ<10.0

Ha:

μ≥10.0

H0:

μ≥10.0

Ha:

μ<10.0

H0:

μ>10.0

Ha:

μ≤10.0

H0:

μ=10.0

Ha:

μ≠10.0

H0:

μ≠10.0

Ha:

μ=10.0

H0:

μ≤10.0

Ha:

μ>10.0

(b) Use technology to find the P-value.

P=nothing

(Round to three decimal places as needed.)

Which of the following is correct?

Reject

because the P-value is

greater than

the significance level.

Fail to reject

because the P-value is

less than

the significance level.

Reject

because the P-value is

less than

the significance level.

Fail to reject

because the P-value is

greater than

the significance level.

(d) Interpret the decision in the context of the original claim.

At the

level of significance, there

is not

sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is

10.0.

At the

level of significance, there

sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is

greater than

10.0.

At the

level of significance, there

sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is

10.0.

At the

level of significance, there

is not

sufficient evidence to reject the claim that the mean number of classroom hours per week for full-time faculty is

less than

10.0.

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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