a) what is the null hypothesisb) what is the alternative hypothesisc) sample meand) test statistic ### SAT Score Analysis for Mathematics Majors**Overview:**A university's Department of Mathematics claims that the mean SAT score for its majors is at least 600. The Admissions department aims to verify this claim by testing it at a 0.10 significance level using a random sample of 16 students.**Data Collection:**The SAT scores for the sample of 16 math majors are as follows:- **Row 1:** 600, 600, 580, 570, 610, 620, 560, 630- **Row 2:** 650, 610, 570, 610, 550, 560, 580, 620**Statistical Assumptions:**- SAT scores are normally distributed.- The population standard deviation is 15.**Objective:**To determine if the university's claim that the mean SAT score is at least 600 is statistically reasonable based on the sample data.

Solution: Given information: n=16 Sample size μ=600 Population mean σ= 15 Population standard…

Answered: A Department of Mathematics at a…

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

a) what is the null hypothesis

b) what is the alternative hypothesis

c) sample mean

d) test statistic

### SAT Score Analysis for Mathematics Majors

**Overview:**
A university's Department of Mathematics claims that the mean SAT score for its majors is at least 600. The Admissions department aims to verify this claim by testing it at a 0.10 significance level using a random sample of 16 students.

**Data Collection:**
The SAT scores for the sample of 16 math majors are as follows:

- **Row 1:** 600, 600, 580, 570, 610, 620, 560, 630
- **Row 2:** 650, 610, 570, 610, 550, 560, 580, 620

**Statistical Assumptions:**
- SAT scores are normally distributed.
- The population standard deviation is 15.

**Objective:**
To determine if the university's claim that the mean SAT score is at least 600 is statistically reasonable based on the sample data.

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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