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Name: A psychologist has designed a psychotherapy programme for people suffe
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Description: A psychologist has designed a psychotherapy programme for people suffering from obesity, and wanted to determine what the mean weight loss would be for a population of people with obesity following the programme. The weight loss in kilograms, of 13 p

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter8: Sequences, Series, And Probability

Section8.7: Probability

Problem 8E: List the sample space of each experiment. Picking a one-digit number

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A psychologist has designed a psychotherapy programme for people suffering from obesity, and wanted to determine what the mean weight loss would be for a population of people with obesity following the programme. The weight loss in kilograms, of 13 people who suffered with obesity and participated in the programme were randomly selected and the results were as follows:
21.4
23.1
25.9
24.7
23.4
24.5
21.9
25.0 22.5 29.9 29.4 25.8 23.2

Question 1

Calculate the mean weight loss for the sample of 13 people (rounded off to four decimals)

Question 2
Calculate the standard deviation for the weight loss data set (rounded off to four decimals).

Question 3
Calculate and interpret a 90% confidence interval for the mean weight loss of the population of obese people following the programme (rounded off to two decimals).

Question 4
The psychologist claims that obese people participating in her psychotherapy programme will have an average weight loss more than 20.5 kilograms. Test the psychologist claim at a 1% level of significance (rounded off to two decimals).

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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