Hypothesis Test Consider the information above and in question 1. It is conjectured that the mean number of people attending all 2017 Veterans Day celebrations is 145, and of interest is to test this conjecture versus the alternative that the mean number of people attending all 2017 Veterans Day celebrations is different from 145 people To test the hypothesis, a simple random sample of 41 Veterans Day celebrations was selected and the number of people attending each was recorded. The mean number of people attending for this sample of 41 celebrations was 157, with a standard deviation of 23 people. The distribution of the data was bimodal. If appropriate, use this information to test the hypotheses stated in question 3 at the a = .05 level of significance. Now suppose of interest is to estimate the mean number of children attending all 2017 Veterans Day celebrations. For this problem only, assume that the standard deviation of the number of children attending all 2017 Veterans Day celebrations is 21. What is the minimum number of 2017 Veterans Day celebrations that would need to be selected for the sample to allow the calculation of a 98% confidence interval with margin of error no larger than 8. a) 37.28 b) 37 c) 18.03 d) 38 e) 18 f) 19

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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Hypothesis Test

Consider the information above and in question 1. It is conjectured that the mean number of people attending all 2017 Veterans Day celebrations is 145, and of interest is to test this conjecture versus the alternative that the mean number of people attending all 2017 Veterans Day celebrations is different from 145 people

To test the hypothesis, a simple random sample of 41 Veterans Day celebrations was selected and the number of people attending each was recorded. The mean number of people attending for this sample of 41 celebrations was 157, with a standard deviation of 23 people. The distribution of the data was bimodal. If appropriate, use this information to test the hypotheses stated in question 3 at the a = .05 level of significance.

Now suppose of interest is to estimate the mean number of children attending all 2017 Veterans Day celebrations. For this problem only, assume that the standard deviation of the number of children attending all 2017 Veterans Day celebrations is 21. What is the minimum number of 2017 Veterans Day celebrations that would need to be selected for the sample to allow the calculation of a 98% confidence interval with margin of error no larger than 8.

a) 37.28

b) 37

c) 18.03

d) 38

e) 18

f) 19

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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