The mean SAT score in mathematics is 507 . The standard deviation of these scores is 36 . A special preparation course claims that the mean SAT score, μ , of its graduates is greater than 507 . An independent researcher tests this by taking a random sample of 150 students who completed the course; the mean SAT score in mathematics for the sample was 510 . At the 0.05 level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than 507 ? Assume that the population standard deviation of the scores of course graduates is also 36 . Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H0 and the alternative hypothesis H1 . H0: H1: (b) Determine the type of test statistic to use. ▼(Choose one) (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 507 ? Yes No

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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Question

The mean SAT score in mathematics is

507

. The standard deviation of these scores is

. A special preparation course claims that the mean SAT score,

, of its graduates is greater than

507

. An independent researcher tests this by taking a random sample of

150

students who completed the course; the mean SAT score in mathematics for the sample was

510

. At the

0.05

level of significance, can we conclude that the population mean SAT score for graduates of the course is greater than

507

? Assume that the population standard deviation of the scores of course graduates is also

Perform a one-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	▼(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)

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

(e)	Can we support the preparation course's claim that the population mean SAT score of its graduates is greater than 507 ?
Yes No

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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