Answered: math teacher claims that she has…

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

math teacher claims that she has developed a review course that increases the scores of students on the math portion of a college entrance exam. Based on data from the administrator of the exam, scores are normally distributed with

μ=519.

The teacher obtains a random sample of

2000

students, puts them through the reviewclass, and finds that the mean math score of the

2000

students is

524

with a standard deviation of

110.

Complete parts (a) through (d) below.

(a) State the null and alternative hypotheses. Let

be the mean score. Choose the correct answer below.

H0: μ<519,

H1: μ>519

H0: μ=519,

H1: μ≠519

H0: μ=519,

H1: μ>519

H0: μ>519,

H1: μ≠519

(b) Test the hypothesis at the α=0.10
level of significance. Is a mean math score of

524

statistically significantly higher than

519?

Conduct a hypothesis test using the P-value approach.

Find the test statistic.

t0=

Approximate the P-value corresponding to the critical value of t.

The P-value is

Is the sample mean statistically significantly higher?

524

versus

519

will affect the decision of a school admissions administrator? In other words, does the increase in the score have any practical significance?

No, because the score became only

0.96%

greater.

Yes, because every increase in score is practically significant.

(d) Test the hypothesis at the

α=0.10

level of significance with

n=375

students. Assume that the sample mean is still

524

and the sample standard deviation is still

110.

Is a sample mean of

524

significantly more than

519?

Conduct a hypothesis test using the P-value approach.

Find the test statistic.

t0=

(Round to two decimal places as needed.)

Approximate the P-value corresponding to the critical value of t.

The P-value is

Is the sample mean statistically significantly higher?

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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