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 44 calls they received was 15 minutes. Test whether the length of calls has changed using the 5% significance level. Complete parts (a) through (d). (a) Carry out a Z test using the five steps of hypothesis testing. Determine a research hypothesis and a null hypothesis. Choose the correct answer below. A. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is less than the mean of the sample population. B. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same. C. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is greater than the mean of the sample population. D. The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same. Assume that the distribution of means is approximately normal. What are the cutoff sample scores on the comparison distribution at which the null hypothesis should be rejected? nothing (Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed.) Determine the sample's Z score on the comparison distribution. Z=nothing (Type an integer or a decimal rounded to two decimal places as needed.) Decide whether to reject the null hypothesis. Explain. Choose the correct answer below. A. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is supported. B. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is false. C. The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true. D. The sample score is not extreme enough to reject the null hypothesis. The experiment in inconclusive

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 44 calls they received was 15 minutes. Test whether the length of calls has changed using the 5% significance level. Complete parts (a) through (d). (a) Carry out a Z test using the five steps of hypothesis testing. Determine a research hypothesis and a null hypothesis. Choose the correct answer below. A. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is less than the mean of the sample population. B. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same. C. The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is greater than the mean of the sample population. D. The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same. Assume that the distribution of means is approximately normal. What are the cutoff sample scores on the comparison distribution at which the null hypothesis should be rejected? nothing (Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed.) Determine the sample's Z score on the comparison distribution. Z=nothing (Type an integer or a decimal rounded to two decimal places as needed.) Decide whether to reject the null hypothesis. Explain. Choose the correct answer below. A. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is supported. B. The sample score is extreme enough to reject the null hypothesis. The research hypothesis is false. C. The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true. D. The sample score is not extreme enough to reject the null hypothesis. The experiment in inconclusive

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section: Chapter Questions

Problem 22SGR

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Question

100%

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. Complete parts (a) through (d).

(a) Carry out a Z test using the five steps of hypothesis testing. Determine a research hypothesis and a null hypothesis. Choose the correct answer below.

The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is less than the mean of the sample population.

The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the populations are not the same.

The research hypothesis is the mean of the populations are the same. The null hypothesis is the mean of the general population is greater than the mean of the sample population.

The research hypothesis is the mean of the populations are not the same. The null hypothesis is the mean of the populations are the same.

Assume that the distribution of means is approximately normal. What are the cutoff sample scores on the comparison distribution at which the null hypothesis should be rejected?

nothing

(Type integers or decimals rounded to two decimal places as needed. Use a comma to separate answers as needed.)

Determine the sample's Z score on the comparison distribution.

Z=nothing

(Type an integer or a decimal rounded to two decimal places as needed.)

Decide whether to reject the null hypothesis. Explain. Choose the correct answer below.

The sample score is extreme enough to reject the null hypothesis. The research

hypothesis is supported.

The sample score is extreme enough to reject the null hypothesis. The research hypothesis is false.

The sample score is not extreme enough to reject the null hypothesis. The research hypothesis is true.

The sample score is not extreme enough to reject the null hypothesis. The experiment in inconclusive

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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