Answered: a. A local health center noted that in…

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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Question

a. A local health center noted that in a sample of 400 patients, the average sample age is 30 years with a population standard deviation of 4.4. (Section 6.1) i.Calculate the standard deviation of the sample mean of patients in the study. ii)Provide a 95% confidence interval for the average age of all the patients who are referred to the health center by the hospital.

b. At a local university, a sample of 49 evening students was selected in order to determine whether the average age of the students is significantly different from 21 years. The average age of the students in the sample was 23 years with a population standard deviation of 3.5 years.

Formulate the null and alternative hypotheses for this problem.

i. Compute the test statistic.

ii. Test these hypotheses and determine the p-value.

iii. State your conclusion. Let alpha (α)= 0.05.

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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