Answered: On their website, a property management…

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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On their website, a property management company states that the mean monthly rent for apartments on the east side of town is $675. A researcher for a consumer advocacy group believes that, due to the construction of newer apartment complexes in neighboring towns, the mean monthly rent on the east side, μ, is now lower. A random sample of 10 monthly rents for apartments on the east side has a mean of $668, with a standard deviation of $24. Assume that current monthly rents for apartments on the east side are approximately normally distributed. Based on the sample, is there enough evidence to conclude, at the 0.10 level of significance, that the population mean monthly rent is now less than what is stated on the website? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places.

A. Find the value of the test statistic and round to 3 or more decimal places. (I have posted a picture of an example problem and the equation to use, with the correct answer as every expert I have asked thus far has gotten this problem wrong.)

B. Find the p-value. (Round to three or more decimal places.)

The Journal de Botanique reported that the mean height of Begonias grown while being treated with a
particular nutrient is 36 centimeters. To check whether this is still accurate, heights are measured for a
random sample of 14 Begonias grown while being treated with the nutrient. The sample mean and sample
standard deviation of those height measurements are 32 centimeters and 11 centimeters, respectively.
Assume that the heights of treated Begonias are approximately normally distributed. Based on the sample,
can it be concluded that the population mean height of treated begonias, µ, is different from that reported in
the journal? Use the 0.10 level of significance. Perform a two-tailed test. Then complete the parts below. Carry
your intermediate computations to three or more decimal places.
MATL
BU
Ch

(c) Finding the value of the test statistic
Since we're assuming the null is true, we use μ = 36. We also have that x = 32, s = 11, and n = 14. So we get the following.
32-36
11
✓√14
t
x-μ
S
√n
≈ 1.361

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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