For all hypothesis testing, you must use the five-step method.You are told that the population mean for the Law School Admissions Test (LSAT) for Canadian students is 429.You want to compare the population of UWO students with Canadian students as a whole with regard to LSAT scores. To find out, you take a random sample of 100 UWO students who have taken the test and find that the sample mean is 462. The population standard deviation is 81. Do UWO students score higher on the LSAT than students from Canada as a whole? You think they do. Use α = .05, and round to three places of the decimal. Interpret your results.

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Description: For all hypothesis testing, you must use the five-step method.You are told that the population mean for the Law School Admissions Test (LSAT) for Canadian students is 429.You want to compare the population of UWO students with Canadian students as a

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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For all hypothesis testing, you must use the five-step method.

You are told that the population mean for the Law School Admissions Test (LSAT) for Canadian students is 429.You want to compare the population of UWO students with Canadian students as a whole with regard to LSAT scores. To find out, you take a random sample of 100 UWO students who have taken the test and find that the sample mean is 462. The population standard deviation is 81. Do UWO students score higher on the LSAT than students from Canada as a whole? You think they do. Use α = .05, and round to three places of the decimal. Interpret your results.

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 + ...

Expert Solution

Step 1

Given information:

The test claim is UWO students score higher on the Law School Admissions Test (LSAT) than students from Canada.

The sample mean, $\bar{x}$ is 462.

The population standard deviation, $σ$ is 81.

The population mean for the law school admission test (LSAT) for Canadian students is 429.

The five step testing procedure is:

(1)The statistical hypothesis is:

The null and alternate hypothesis for the test is,

$μ = 429 μ > 429$

It is a right-tailed test.

(2)Rejection Region

The level of significance for the test statistics is 5% i.e. 0.05 .

The critical value of Z statistics at 0.05 level of significance is 1.64.

Thus, any value of calculated z statistics above $\pm$ 1.64 will lie in the rejection region and will result in the rejection of null hypothesis at $α = 0.05$ .

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