You may need to use the appropriate appendix table or technology to answer this question. Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 13 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys from a particular client provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with σ = 9 minutes. Is the premium rate justified for this client? 17 11 12 23 20 23 15 16 23 22 18 23 25 14 12 12 20 18 12 19 11 11 20 21 11 18 14 13 13 19 16 10 22 18 23 (a) Formulate the null and alternative hypotheses for this application. H0: μ > 13 Ha: μ ≤ 13 H0: μ = 13 Ha: μ ≠ 13 H0: μ ≤ 13 Ha: μ > 13 H0: μ < 13 Ha: μ ≥ 13 H0: μ ≥ 13 Ha: μ < 13 (b) Compute the value of the test statistic. (Round your answer to two decimal places.) (c) What is the p-value? (Round your answer to four decimal places.) p-value = (d) At ? = 0.01, what is your conclusion? Do not reject H0. There is sufficient evidence to conclude that the premium rate should be charged.Reject H0. There is insufficient evidence to conclude that the premium rate should be charged. Do not reject H0. There is insufficient evidence to conclude that the premium rate should be charged.Reject H0. There is sufficient evidence to conclude that the premium rate should be charged.

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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You may need to use the appropriate appendix table or technology to answer this question.

Fowle Marketing Research, Inc., bases charges to a client on the assumption that telephone surveys can be completed in a mean time of 13 minutes or less. If a longer mean survey time is necessary, a premium rate is charged. A sample of 35 surveys from a particular client provided the survey times shown in the file named Fowle. Based upon past studies, the population standard deviation is assumed known with

σ = 9 minutes.

Is the premium rate justified for this client?

17	11	12	23	20	23	15
16	23	22	18	23	25	14
12	12	20	18	12	19	11
11	20	21	11	18	14	13
13	19	16	10	22	18	23

(a)

Formulate the null and alternative hypotheses for this application.

H₀: μ > 13

H_a: μ ≤ 13

H₀: μ = 13

H_a: μ ≠ 13

H₀: μ ≤ 13

H_a: μ > 13

H₀: μ < 13

H_a: μ ≥ 13

H₀: μ ≥ 13

H_a: μ < 13

(b)

Compute the value of the test statistic. (Round your answer to two decimal places.)

(c)

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

p-value =

(d)

? = 0.01,

what is your conclusion?

Do not reject H₀. There is sufficient evidence to conclude that the premium rate should be charged.Reject H₀. There is insufficient evidence to conclude that the premium rate should be charged. Do not reject H₀. There is insufficient evidence to conclude that the premium rate should be charged.Reject H₀. There is sufficient evidence to conclude that the premium rate should be charged.

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 + ...

Expert Solution

Step 1

Sample size = n = 35.

Sample mean:

$\begin{array}{rcl} x & = & \frac{\sum_{} x}{n} \\ = & \frac{595}{35} \\ = & 17 \end{array}$

Step 2

(a)

Hypothesis to be tested:

H₀: μ ≤ 13

H_a: μ > 13

Step 3

(b)

Test statistic:

$\begin{array}{rcl} z & = & \frac{x - μ}{\frac{σ}{\sqrt{n}}} \\ = & \frac{17 - 13}{\frac{9}{\sqrt{35}}} \\ = & 2.63 \end{array}$

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