Answered: At a large furniture and electrical…

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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Related questions

Question

At a large furniture and electrical store, customers usually find that the furniture on display is not held in stock. Rather than being immediately available, it must be sourced from manufacturers. In the sofa department, the average delivery time is expected to be

six

weeks after purchase. In order to test whether this target is accurate, the store records the delivery times (in days) taken for

sofa purchases. Complete parts (a) through (d).

Click the icon to view the data table.

a. The supervisor claims that the mean number of days between receipt of the order and delivery of the sofa is

days or more. At the

0.05

level of significance, is there evidence that the claim is not true (that is, that the mean number of days is less than

42)?

State the null and alternative hypotheses. Choose the correct answer below.

H0:

μ>42

H1:

μ<42

H0:

μ≠42

H1:

μ=42

H0:

μ≤42

H1:

μ>42

H0:

μ>42

H1:

μ≤42

H0:

μ≥42

H1:

μ<42

H0:

μ=42

H1:

μ≠42

Determine the test statistic.

The test statistic is

enter your response here.

(Round to two decimal places as needed.)

Find the p-value.

p-value=enter your response here

(Round to three decimal places as needed.)

State the conclusion.

▼

Do not reject

Reject

H0.

There is

▼

insufficient

sufficient

evidence to conclude that the mean number of days is less than

42.

b. What assumption about the population distribution is needed in order to conduct the t test in (a)?

The population distribution is approximately normal.

The population distribution is approximately uniform.

The population distribution is skewed left.

The population distribution is skewed right.

c. Do you think that the assumption needed in (b) is seriously violated? Explain.

Construct a normal probability plot to evaluate the assumption made in (b). Choose the correct graph below.

Normal probability plot

0-2.52.50175Z valueTime (in days)

x y graph

Normal probability plot

0-2.52.50175Z valueTime (in days)

x y graph

Normal probability plot

0-2.52.50175Z valueTime (in days)

x y graph

Do you think that the assumption needed in (b) is seriously violated? Explain. Choose the correct answer below.

No, because the normal probability plot is a straight line.

No, because the normal probability plot is not a straight line.

Yes, because the normal probability plot is a straight line.

Yes, because the normal probability plot is a not straight line.

d. What effect might your conclusion in (c) have on the validity of the results in (a)?

The population distribution is approximately normal, so the t test is valid.

The population distribution is not approximately normal, so the t test is not valid.

Although the normal probability plot is a straight line, the sample size is greater than 30, so the Central Limit Theorem applies and the results of the t test are still valid.

Although the normal probability plot is not a straight line, the sample size is greater than 30, so the Central Limit Theorem applies and the results of the t test are still valid.

At a large furniture and electrical store, customers usually find that the furniture on display is not held in stock. Rather than being immediately available, it must be sourced from manufacturers. In the sofa department, the average delivery time is
expected to be six weeks after purchase. In order to test whether this target is accurate, the store records the delivery times (in days) taken for 50 sofa purchases. Complete parts (a) through (d).
E Click the icon to view the data table.
c. Do you think that the assumption needed in (b) is seriously violated? Explain.
Construct a normal probability plot to evaluate the assumption made in (b). Choose the correct graph below.
O A.
OB.
Oc.
Normal probability
plot
Normal probability
plot
Normal probability
plot
175-
175-
175-
0+
-2.5
0+
-2.5
0-
-2.5
2.5
2.5
Z value
Z value
Z value
Do you think that the assumption needed in (b) is seriously violated? Explain. Choose the correct answer below.
O A. No, because the normal probability plot is a straight line.
O B. No, because the normal probability plot is not a straight line.
Oc. Yes, because the normal probability plot is a straight line.
O D. Yes, because the normal probability plot is a not straight line.
d. What effect might your conclusion in (c) have on the validity of the results in (a)?
O A. The population distribution is approximately normal, so the t test is valid.
O B. The population distribution is not approximately normal, so the t test is not valid.
OC. Although the normal probability plot is a straight line, the sample size is greater than 30, so the Central Limit Theorem applies and the results of the t test are still valid.
O D. Although the normal probability plot is not a straight line, the sample size
greater than 30, so the Central Limit Theorem applies and the results of the t test are still valid.
Time (in days)
ime (in days)
Time (in days)

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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