Suppose that scores on the Scholastic Aptitude Test form a normal distribution with m = 500 and s = 100. A high school counselor has developed a special course designed to boost SAT scores. A random sample of 16 students is selected to take the course and then the SAT. The sample had an average score of 544. Test the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500. Test at a significance level of a = 0.01. a) State the claim and the opposite H0:H1: What is the significance level Calculate the test- statistic (use formula for population mean) What is the p-value? (remember to check if it is left, right or 2 tail) Do we reject or fail to reject H0? Which is the correct interpretation (circle the correct answer) There is enough evidence to support the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500.ii) There is not enough evidence to support the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500.

sample size (n) = 16 sample mean (x̄) = 544 sample standard deviation (s) = 100 population mean (…

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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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Suppose that scores on the Scholastic Aptitude Test form a normal distribution with m = 500 and s = 100. A high school counselor has developed a special course designed to boost SAT scores. A random sample of 16 students is selected to take the course and then the SAT. The sample had an average score of 544. Test the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500. Test at a significance level of a = 0.01.

a) State the claim and the opposite

H₀:

H₁:

What is the significance level

Calculate the test- statistic (use formula for population mean)

What is the p-value? (remember to check if it is left, right or 2 tail)

Do we reject or fail to reject H₀?

Which is the correct interpretation (circle the correct answer)

There is enough evidence to support the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500.
ii) There is not enough evidence to support the claim that someone who takes the Scholastic Aptitude Test will get a score greater than 500.

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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