Answered: A certain statistics professor believes…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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A certain statistics professor believes that the scores on her final exam (scored out of 80 points) have a normal distribution with a mean of 60 points and a standard deviation of 8.5 points. sample of 16 students from her classes: Suppose the following is the final exam scores of a random 45.6 51.2 55.1 56.1 56.8 57.6 58.3 58.5 60.7 62.4 64.9 68.7 69.6 73.6 76.5 79.2 1) Calculate the mean and standard deviation of this data set. these are Do you think reasonable given the assumed distribution and size of the data set? 2) Use the previous data to calculate a 95% confidence interval for the true mean score for this exam (do not assume a is known). Is the assumed mean (60) in the interval? 3) If we want the previous confidence interval to have a margin of error less than 2 points, how many students should be sampled? In recent poling, it has been suggested that the approval rating of a certain politician (the proportion of people polled that approve of his performance in office) is around 40%. 4 After taking the new poll, we find that 11 out of the 37 people polled approve of the politician's performance in office. Calculate a 95% confidence interval for the true approval rating (or rather, the population proportion of people who approve of the politician's performance) . 5) If we want the margin of error in the previous interval to be less than 3%, how many people should we poll in total? 6) Does 40% fall into the confidence interval in problem 15? Does this suggest that the politician's approval rating has fallen significantly?

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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