A telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. Over the past several years, the lengths of telephone calls (in minutes) were normally distributed withμ=14andσ=8.The service arranged to have the special phone system loaned to them for one day. On that day, the mean length of the44calls they received was15minutes. Test whether the length of calls has changed using the 5% significance level. (b) Make a drawing of the distributions. The distribution of the general population is in blue and the distribution of means is in black. Choose the correct answer below.A.O B.OC.D.1415311424(c) Explain your answer to someone who knows about hypothesis testing with a sample of a single individual but who knows nothing about hypothesis testing withsamples of more than one individual,The distribution of means uses many samples ofV with each sample randomly taken from the population of individuals. Since the sample score couldV the hypothesis that the length of calls is affected by better call sound quality. In this situation,the researcher is finding a Z score of the sample's mean on a distribution of means instead of finding the Z score of a single individual on a distribution of singleoccur by chanceV the resultsindividuals. The sample mean is being treated as(d) Figure the 95% confidence interval.One can be 95% confident that the true population mean is betweenand(Type integers or decimals rounded to two decimal places as needed.)

Null Hypothesis: A hypothesis which is tested for plausible rejection is called the Null Hypothesis…

Answered: A telephone counseling service for…

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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A telephone counseling service for adolescents tested whether the length of calls would be affected by a special telephone system that had a better sound quality. Over the past several years, the lengths of telephone calls (in minutes) were normally distributed with

μ=14

and

σ=8.

The service arranged to have the special phone system loaned to them for one day. On that day, the mean length of the

calls they received was

minutes. Test whether the length of calls has changed using the 5% significance level.

(b) Make a drawing of the distributions. The distribution of the general population is in blue and the distribution of means is in black. Choose the correct answer below.
A.
O B.
OC.
D.
14
15
31
14
24
(c) Explain your answer to someone who knows about hypothesis testing with a sample of a single individual but who knows nothing about hypothesis testing with
samples of more than one individual,
The distribution of means uses many samples of
V with each sample randomly taken from the population of individuals. Since the sample score could
V the hypothesis that the length of calls is affected by better call sound quality. In this situation,
the researcher is finding a Z score of the sample's mean on a distribution of means instead of finding the Z score of a single individual on a distribution of single
occur by chance
V the results
individuals. The sample mean is being treated as
(d) Figure the 95% confidence interval.
One can be 95% confident that the true population mean is between
and
(Type integers or decimals rounded to two decimal places as needed.)

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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