Listed below are fair market values (in thousands of dollars) of randomly selected homes on Long Beach Island in New Jersey. Use a 0.05 significance level to test a realtor's claim that ocean front homes (directly on the beach) have greater value than oceanside homes, which are not directly on the beach. Oceanfront: 2199 3750 1725 2398 2799Oceanside: 700 1355 795 1575 759a. Define the parameters A.mu 1 equals The mean value of the oceanfront homes in this samplemu 2 equals The mean value of the oceanside homes in this sample B.mu 1 equals The mean value of all oceanfront homes on Long Beach Islandmu 2 equals The mean value of all oceanside homes on Long Beach Island C.p 1 equals The proportion of homes that are oceanfrontp 2 equals The proportion of homes that are oceanside D.mu 1 equals The mean number of oceanfront homesmu 2 equals The mean number of oceanside homes b. State the null and alternative hypotheses A.Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2 B.Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 greater than p 2 C.Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2 D.Upper H 0 : mu 1 equals 2199 Upper H 1 : mu 2 equals 700 c. Calculate the mean and standard deviation of each sample (round each to 1 decimal place): Oceanfront:x overbar equalsnothing s = nothingOceanside: x overbar equalsnothing s = nothing d. Calculate the P-value. Which of these options is closest to its value? A.negative 0.0052 B.0.0990 C.0.0035 D.0.2911 e. State the technical conclusion A.Reject Upper H 0 B.Do not reject Upper H 0 f. State the final conclusion A.There is sufficient evidence to warrant rejection of the claim. B.There is not sufficient sample evidence to support the claim. C.There is not sufficient evidence to warrant rejection of the claim. D.The sample data support the claim. g. Given that there are only five values in each sample, can we really conclude that oceanfront homes have a greater mean value? A.Yes, the large difference in the sample means more than compensates for the fact that the samples are small B.No, these samples are too small

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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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Listed below are fair market values (in thousands of dollars) of randomly selected homes on Long Beach Island in New Jersey. Use a 0.05 significance level to test a realtor's claim that ocean front homes (directly on the beach) have greater value than oceanside homes, which are not directly on the beach.

Oceanfront: 2199 3750 1725 2398 2799

Oceanside: 700 1355 795 1575 759

a. Define the parameters

mu 1 equals

The mean value of the oceanfront homes in this sample

mu 2 equals

The mean value of the oceanside homes in this sample

mu 1 equals

The mean value of all oceanfront homes on Long Beach Island

mu 2 equals

The mean value of all oceanside homes on Long Beach Island

p 1 equals

The proportion of homes that are oceanfront

p 2 equals

The proportion of homes that are oceanside

mu 1 equals

The mean number of oceanfront homes

mu 2 equals

The mean number of oceanside homes

b. State the null and alternative hypotheses

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 greater than mu 2

Upper H 0 : p 1 equals p 2 Upper H 1 : p 1 greater than p 2

Upper H 0 : mu 1 equals mu 2 Upper H 1 : mu 1 less than mu 2

Upper H 0 : mu 1 equals 2199

Upper H 1 : mu 2 equals 700

c. Calculate the mean and standard deviation of each sample (round each to 1 decimal place):

Oceanfront:

x overbar equals

nothing

s = nothingOceanside:

x overbar equals

nothing

s = nothing

d. Calculate the P-value. Which of these options is closest to its value?

negative 0.0052

0.0990

0.0035

0.2911

e. State the technical conclusion

Reject Upper H 0

Do not reject Upper H 0

f. State the final conclusion

There is sufficient evidence to warrant rejection of the claim.

There is not sufficient sample evidence to support the claim.

There is not sufficient evidence to warrant rejection of the claim.

The sample data support the claim.

g. Given that there are only five values in each sample, can we really conclude that oceanfront homes have a greater mean value?

Yes, the large difference in the sample means more than compensates for the fact that the samples are small

No, these samples are too small

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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