You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 24 Model A washing machines is $209. Assume the population standard deviation is $20. The mean repair cost of 27 Model B washing machines is $215. Assume the population standard deviation is $24. At α=0.01, can you reject the salesperson's claim? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. What is the claim? A. The mean repair costs for Model A and Model B are equal. B. The mean repair cost for Model A is greater than Model B. C. The mean repair costs for Model A and Model B are different. D. The mean repair cost for Model A is less than Model B. Let μ1 be the mean repair cost for Model A and let μ2 be the mean repair cost for Model B. What are H0 and Ha? A. H0: μ1≤μ2 Ha: μ1>μ2 B. H0: μ1≥μ2 Ha: μ1<μ2 C. H0: μ1≠μ2 Ha: μ1=μ2 D. H0: μ1<μ2 Ha: μ1≥μ2 E. H0: μ1=μ2 Ha: μ1≠μ2 F. H0: μ1>μ2 Ha: μ1≤μ2 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are negative 2.58 comma 2.58−2.58,2.58. (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is/are the rejection region(s)? Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. z2.582.58 B. znothing (c) Find the standardized test statistic z for μ1−μ2. z=negative . 15−.15 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. A. Reject H0. The standardized test statistic is not in a rejection region. B. Fail to reject H0. The standardized test statistic is not in a rejection region. C. Reject H0. The standardized test statistic is in a rejection region. D. Fail to reject H0. The standardized test statistic is in a rejection region. (e) Interpret the decision in the context of the original claim. At the 11% significance level, there is insufficient insufficient sufficient evidence to reject support reject the claim that the mean repair costs for Model A are equal to equal to less than greater than different from the mean repair costs for Model B.

You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of 24 Model A washing machines is $209. Assume the population standard deviation is $20. The mean repair cost of 27 Model B washing machines is $215. Assume the population standard deviation is $24. At α=0.01, can you reject the salesperson's claim? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. What is the claim? A. The mean repair costs for Model A and Model B are equal. B. The mean repair cost for Model A is greater than Model B. C. The mean repair costs for Model A and Model B are different. D. The mean repair cost for Model A is less than Model B. Let μ1 be the mean repair cost for Model A and let μ2 be the mean repair cost for Model B. What are H0 and Ha? A. H0: μ1≤μ2 Ha: μ1>μ2 B. H0: μ1≥μ2 Ha: μ1<μ2 C. H0: μ1≠μ2 Ha: μ1=μ2 D. H0: μ1<μ2 Ha: μ1≥μ2 E. H0: μ1=μ2 Ha: μ1≠μ2 F. H0: μ1>μ2 Ha: μ1≤μ2 (b) Find the critical value(s) and identify the rejection region(s). The critical value(s) is/are negative 2.58 comma 2.58−2.58,2.58. (Round to two decimal places as needed. Use a comma to separate answers as needed.) What is/are the rejection region(s)? Select the correct choice below and fill in the answer box(es) within your choice. (Round to two decimal places as needed.) A. z2.582.58 B. znothing (c) Find the standardized test statistic z for μ1−μ2. z=negative . 15−.15 (Round to two decimal places as needed.) (d) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below. A. Reject H0. The standardized test statistic is not in a rejection region. B. Fail to reject H0. The standardized test statistic is not in a rejection region. C. Reject H0. The standardized test statistic is in a rejection region. D. Fail to reject H0. The standardized test statistic is in a rejection region. (e) Interpret the decision in the context of the original claim. At the 11% significance level, there is insufficient insufficient sufficient evidence to reject support reject the claim that the mean repair costs for Model A are equal to equal to less than greater than different from the mean repair costs for Model B.

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 26PFA

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Question

You want to buy a washing machine, and a salesperson tells you that the mean repair costs for Model A and Model B are equal. You research the repair costs. The mean repair cost of

Model A washing machines is

$209.

Assume the population standard deviation is

$20.

The mean repair cost of

Model B washing machines is

$215.

Assume the population standard deviation is

$24.

α=0.01,

can you reject the salesperson's claim? Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e).

(a) Identify the claim and state

and

Ha.

What is the claim?

The mean repair costs for Model A and Model B are equal.

The mean repair cost for Model A is greater than Model B.

The mean repair costs for Model A and Model B are different.

The mean repair cost for Model A is less than Model B.

Let

μ1

be the mean repair cost for Model A and let

μ2

be the mean repair cost for Model B. What are

and

Ha?

H0:

μ1≤μ2

Ha:

μ1>μ2

H0:

μ1≥μ2

Ha:

μ1<μ2

H0:

μ1≠μ2

Ha:

μ1=μ2

H0:

μ1<μ2

Ha:

μ1≥μ2

H0:

μ1=μ2

Ha:

μ1≠μ2

H0:

μ1>μ2

Ha:

μ1≤μ2

(b) Find the critical value(s) and identify the rejection region(s).

The critical value(s) is/are

negative 2.58 comma 2.58−2.58,2.58.

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

What is/are the rejection region(s)? Select the correct choice below and fill in the answer box(es) within your choice.

(Round to two decimal places as needed.)

z<negative 2.58−2.58,

z>2.582.58

z<nothing

z>nothing

μ1−μ2.

z=negative . 15−.15

(Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

Reject

H0.

The standardized test statistic

is not

in a rejection region.

Fail to reject

H0.

The standardized test statistic

is not

in a rejection region.

Reject

H0.

The standardized test statistic

in a rejection region.

Fail to reject

H0.

The standardized test statistic

in a rejection region.

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

At the

11%

significance level, there is

insufficient

sufficient

evidence to

reject

support

reject

the claim that the mean repair costs for Model A are

equal to

less than

greater than

different from

the mean repair costs for Model B.

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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