Answered: The Central Limit Theorem says that…

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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1. The Central Limit Theorem says that

Group of answer choices

the distribution of a sum or proportion of randomly selected observations is always normal

the distribution of a sum or proportion of randomly selected observations is only normal if the randomly selected observations are from a normal distribution

the distribution of a sum or proportion of randomly selected observations eventually gets close to a normal distribution as long as we have a large sample size

2. (Repeated from previous question) A new census bureau reporting method for quantifying the number of "poor" Americans reports 49.1 million people as poor (article linked if you care to read). This is roughly 16% of all Americans.

Suppose a polling company, using the same method for categorizing "poor", wants to take a sample of 1,000 Americans. In the long run (if they were to take many, many samples of size 1,000), we can expect the the distribution of sample proportions (proportion of each sample who are "poor") to have what average value (mean)?

Group of answer choices

49.1 million

1,000

0.16 (or 16%)

sqrt(0.16*(1-0.16)/1000)

3. (Repeated from previous question) A new census bureau repoting method for quantifying the number of "poor" Americans reports 49.1 million people as poor (article linked if you care to read). This is roughly 16% of all Americans.

Group of answer choices

49.1 million

1,000

0.16 (or 16%)

sqrt(0.16*(1-0.16)/1000)

It is OK to interpret a 95% confidence interval starting with "With 95% probability" rather than "With 95% confidence".

Group of answer choices

True

False

Characteristics of a hypothesis test: If a hypothesis test yields a P-value of 0.005,

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the margin of error is 0.005

the null hypothesis is very likely to be true

the alternative hypothesis is very likely to be true

the alternative hypothesis is not very likely to be true

6. In 2006, 75.9% of first-year college students responding to a national survey said that they used the internet frequently for research or homework. You wonder if the proportion of first-year students at this university who said that they used the Internet frequently for research or homework differs from the national value, 75.9 percent.
A random sample form a state university finds that 130 of an SRS of 200 of its first-year students said that they used the Internet frequently for research or homework.
Identify the null hypothesis (H_O).

Group of answer choices

p = 0.759

p < 0.759

p > 0.759

p ≠ 0.759

7. Please refer to the previous problem.
Identify the alternative hypothesis (H_A).

Group of answer choices

p = 0.759

p < 0.759

p > 0.759

p ≠ 0.759

8. The financial aid office of a university asks a sample of graduates about their employment and earnings. They wanted to see if men make more, on average.
The report says, “For academic year earnings, we found on average, men make significantly more money than females (P = 0.028).”
Identify the null hypothesis

Group of answer choices

there is no difference in earnings between males and females (difference = 0)

males earn more than females (males – females > 0)

males earn less than females (males – females < 0)

males earn a different amount than females (males – females ≠ 0)

9. Please refer to the previous problem.
Identify the alternative hypothesis.

Group of answer choices

there is no difference in earnings between males and females (difference = 0)

males earn more than females (males – females > 0)

males earn less than females (males – females < 0)

males earn a different amount than females (males – females ≠ 0)

10. Interpret the P-value for the male and female earnings report.

Group of answer choices

There is a 2.8% chance of seeing earnings this much larger for males if there really was no difference.

There is a 2.8% chance of seeing earnings this much smaller for males if there really was no difference.

There is a 2.8% chance of seeing earnings this much higher for males if there really was a difference.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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