What does the Central Limit Theorem tell about the sample mean? If the sample size is large, the distribution of all individual observations should be normally distributed. If your sample size is large, the distribution of the sample mean should be normally distributed with the population mean as its center. The distribution of the sample mean is always perfectly normally distributed. your sample size is large, the distribution of the population mean should be normally distributed with the population mean as its center.

What does the Central Limit Theorem tell about the sample mean? If the sample size is large, the distribution of all individual observations should be normally distributed. If your sample size is large, the distribution of the sample mean should be normally distributed with the population mean as its center. The distribution of the sample mean is always perfectly normally distributed. your sample size is large, the distribution of the population mean should be normally distributed with the population mean as its center.

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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We want to estimate the mean of a certain population, so we will collect a sample. Which should be true if we use a large sample rather than a small one?I. The distribution of our sample data will be approximately normal.II. The sampling distribution of the sample means will be approximately normal.III. The variability of the sample means will be smaller. only I I, II, and III only III only II II and III
Suppose that, at the end of last semester, Marie gave her introductory statistics class a final exam. After grading these exams, she created a histogram illustrating the distribution of exam scores for the 70 students in the class. Each of the bars in this histogram includes only the left endpoint of the interval, except for the bar representing scores between 90 and 100 points, which also includes the right endpoint. What percentage of students scored between 60 and 80 points on the exam? Round your answer to the nearest tenth of a percent. Number of students who scored at least 80 points = students Percentage of students who scored between 60 and 80 points = %
For data that is not normally distributed we can't use z-scores. However, there is an equation that works on any distribution. It's called Chebyshev's formula. The formula is p = 1 - 7.2 where p is the minimum percentage of scores that fall within k standard deviations on both sides of the mean. Use this formula to answer the following questions. a) If you have scores and you don't know if they are normally distributed, find the minimum percentage of scores that fall within 2.1 standard deviations on both sides of the mean? b) If you have scores that are normally distributed, find the percentage of scores that fall within 2.1 standard deviations on both sides of the mean? c) If you have scores and you don't know if they are normally distributed, how many standard deviations on both sides of the mean do we need to go to have 96 percent of the scores? Note: To answer part c you will need to solve the equation for k.
(c) Determine if the means of samples 1 and 2 overestimate, underestimate, or are equal to the population mean. The mean pulse rate of sample 1 the population mean. The mean pulse rate of sample 2 the population mean.
Explain why this statement is true: Suppose you take large repeated samples of a variable X (which is uniformly distributed). The distribution of the sample means will also be uniform.
The finite population correction is most useful for which of the following? a. It adjusts the estimated mean when the sample size is a large fraction of the population size. b. It adjusts the standard error of the mean when the sample size is a small fraction of the population size. c. It adjusts the estimated mean when the sample size is a small fraction of the population size. d. It adjusts the standard error of the mean when the sample size is a large fraction of the population size.
Suppose that we have disjoint normal populations A and B with equal but unknown population variances. Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance. If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?
To determine whether caffeine consumption affects the ability to solve math problems, a researcher had one group solve math problems after taking a cup of caffeinated drink and another group solves math problems after taking a cup of water. The group who took the caffeinated drink completed 35 problems in one hour and the group that had water completed 20 problems in one hour. Assuming the number of problems solved is normally distributed in each group, what statistical test would be used to test the research hypothesis? Explain your answer.