The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7450 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,230 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7450 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach? e. Compare the results of parts (a) through (d) to those when the standard deviation is 875 hours. a. Let μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ ▼ equals= less than or equals≤ greater than or equals≥ not equals≠ enter your response here H1: μ ▼ not equals≠ equals= greater than> less than< enter your response here Part 2 What is the test statistic? ZSTAT=enter your response here (Round to two decimal places as needed.) Part 3 What is/are the critical value(s)? enter your response here (Round to two decimal places as needed. Use a comma to separate answers as needed.) Part 4 What is the final conclusion? A. Fail to reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. B. Fail to reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. C. Reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. D. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. Part 5 b. What is the p-value? enter your response here (Round to three decimal places as needed.) Part 6 Interpret the meaning of the p-value. The p-value is the probability of obtaining a ▼ sample population with a mean ▼ equal to at least as extreme as less extreme than enter your response here hours, given that the ▼ alternative null hypothesis is true. Part 7 c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. enter your response here≤μ≤enter your response here (Round to the nearest whole number as needed.) Part 8 d. Compare the results of (a) and (c). What conclusions do you reach? A. The results of (a) and (c) are the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. B. The results of (a) and (c) are not the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. C. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. D. The results of (a) and (c) are the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. Part 9 e. Compare the results of parts (a) through (d) to those when the standard deviation is 875. When the standard deviation is 875, ZSTAT=−1.76, the p-value is 0.078, and the 95% confidence interval is 6,985≤μ≤7,475. State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a). Using the critical value approach, ▼ reject do not reject H0. This result is ▼ the same as different from the result found in part (a) because ZSTAT has ▼ increased not changed decreased in absolute value. Part 10 State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b). Using the p-value approach, ▼ do not reject reject H0. This result is ▼ different from the same as the result found in part (b) because the p-value has ▼ not changed. increased. decreased. Part 11 State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c). Using the confidence interval approach, ▼ reject do not reject H0. This result is ▼ different from the same as the result found in part (c), because the confidence interval has ▼ not changed. become narrower. become wider.

The quality-control manager at a compact fluorescent light bulb (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7450 hours. The population standard deviation is 700 hours. A random sample of 49 light bulbs indicates a sample mean life of 7,230 hours. a. At the 0.05 level of significance, is there evidence that the mean life is different from 7450 hours? b. Compute the p-value and interpret its meaning. c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. d. Compare the results of (a) and (c). What conclusions do you reach? e. Compare the results of parts (a) through (d) to those when the standard deviation is 875 hours. a. Let μ be the population mean. Determine the null hypothesis, H0, and the alternative hypothesis, H1. H0: μ ▼ equals= less than or equals≤ greater than or equals≥ not equals≠ enter your response here H1: μ ▼ not equals≠ equals= greater than> less than< enter your response here Part 2 What is the test statistic? ZSTAT=enter your response here (Round to two decimal places as needed.) Part 3 What is/are the critical value(s)? enter your response here (Round to two decimal places as needed. Use a comma to separate answers as needed.) Part 4 What is the final conclusion? A. Fail to reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. B. Fail to reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. C. Reject H0. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. D. Reject H0. There is sufficient evidence to indicate that the mean life is different from 7450 hours. Part 5 b. What is the p-value? enter your response here (Round to three decimal places as needed.) Part 6 Interpret the meaning of the p-value. The p-value is the probability of obtaining a ▼ sample population with a mean ▼ equal to at least as extreme as less extreme than enter your response here hours, given that the ▼ alternative null hypothesis is true. Part 7 c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs. enter your response here≤μ≤enter your response here (Round to the nearest whole number as needed.) Part 8 d. Compare the results of (a) and (c). What conclusions do you reach? A. The results of (a) and (c) are the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. B. The results of (a) and (c) are not the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. C. The results of (a) and (c) are not the same. There is sufficient evidence to indicate that the mean life is different from 7450 hours. D. The results of (a) and (c) are the same. There is not sufficient evidence to indicate that the mean life is different from 7450 hours. Part 9 e. Compare the results of parts (a) through (d) to those when the standard deviation is 875. When the standard deviation is 875, ZSTAT=−1.76, the p-value is 0.078, and the 95% confidence interval is 6,985≤μ≤7,475. State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a). Using the critical value approach, ▼ reject do not reject H0. This result is ▼ the same as different from the result found in part (a) because ZSTAT has ▼ increased not changed decreased in absolute value. Part 10 State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b). Using the p-value approach, ▼ do not reject reject H0. This result is ▼ different from the same as the result found in part (b) because the p-value has ▼ not changed. increased. decreased. Part 11 State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c). Using the confidence interval approach, ▼ reject do not reject H0. This result is ▼ different from the same as the result found in part (c), because the confidence interval has ▼ not changed. become narrower. become wider.

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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Part 2

What is the test statistic?

ZSTAT=enter your response here

(Round to two decimal places as needed.)

Part 3

What is/are the critical value(s)?

enter your response here

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

Part 4

What is the final conclusion?

Fail to reject

H0.

There

is not

sufficient evidence to indicate that the mean life is different from

7450

hours.

Fail to reject

H0.

There

sufficient evidence to indicate that the mean life is different from

7450

hours.

Reject

H0.

There

is not

sufficient evidence to indicate that the mean life is different from

7450

hours.

Reject

H0.

There

sufficient evidence to indicate that the mean life is different from

7450

hours.

Part 5

b. What is the p-value?

enter your response here

(Round to three decimal places as needed.)

Part 6

Interpret the meaning of the p-value.

The p-value is the probability of obtaining a

▼

sample

population

with a mean

▼

equal to

at least as extreme as

less extreme than

enter your response here

hours, given that the

▼

alternative

null

hypothesis is true.

Part 7

c. Construct a 95% confidence interval estimate of the population mean life of the light bulbs.

enter your response here≤μ≤enter your response here

(Round to the nearest whole number as needed.)

Part 8

d. Compare the results of (a) and (c). What conclusions do you reach?

The results of (a) and (c) are the same. There

sufficient evidence to indicate that the mean life is different from

7450

hours.

The results of (a) and (c) are not the same. There

is not

sufficient evidence to indicate that the mean life is different from

7450

hours.

The results of (a) and (c) are not the same. There

sufficient evidence to indicate that the mean life is different from

7450

hours.

The results of (a) and (c) are the same. There

is not

sufficient evidence to indicate that the mean life is different from

7450

hours.

Part 9

e. Compare the results of parts (a) through (d) to those when the standard deviation is

875.

When the standard deviation is

875,

ZSTAT=−1.76,

the p-value is

0.078,

and the 95% confidence interval is

6,985≤μ≤7,475.

State the conclusion for the new standard deviation using the critical value approach. Compare the results to part (a).

Using the critical value approach,

▼

reject

do not reject

H0.

This result is

▼

the same as

different from

the result found in part (a) because

ZSTAT

has

▼

increased

not changed

decreased

in absolute value.

Part 10

State the conclusion for the new standard deviation using the p-value approach. Compare the results to part (b).

Using the p-value approach,

▼

do not reject

reject

H0.

This result is

▼

different from

the same as

the result found in part (b) because the p-value has

▼

not changed.

increased.

decreased.

Part 11

State the conclusion for the new standard deviation using the confidence interval approach. Compare the results to part (c).

Using the confidence interval approach,

▼

reject

do not reject

H0.

This result is

▼

different from

the same as

the result found in part (c), because the confidence interval has

▼

not changed.

become narrower.

become wider.

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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