For a two-tailed hypothesis test at the significance level α,the null hypothesis H0: μ=μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠μ0 if and only if μ0 lies outside the (1−α)-level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean t-interval for the summary statistics provided. Complete parts (a) and (b). According to a survey, the average person watched 4.35 hours of television per day in 2005. A random sample of 20 people were asked for the number of hours of television watched per day for last year. At the 10% significance level, the data do not provide sufficient evidence to conclude that the amount of television watched per day last year by the average person differed from that in 2005. (Note: x=4.752 hours and= s=2.384 hours.) The confidence interval is (Round to three decimal places as needed.) According to a national study the average consumer unit spent $1739 on apparel and services in 2012. That same year, 25 consumer units in the Northeast were surveyed about their annual expenditures, in dollars, on apparel and services. At the 2% significance level, the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1739. (Note: x=$1920.22 and s=$349.83.) The confidence interval is (Round to two decimal places as needed.)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 6CR

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For a two-tailed hypothesis test at the significance level α,the null hypothesis H0: μ=μ0 will be rejected in favor of the alternative hypothesis Ha: μ≠μ0 if and only if μ0 lies outside the (1−α)-level confidence interval for μ. Illustrate the preceding relationship by obtaining the appropriate one-mean t-interval for the summary statistics provided. Complete parts (a) and (b).

According to a survey, the average person watched 4.35 hours of television per day in 2005. A random sample of 20 people were asked for the number of hours of television watched per day for last year. At the 10% significance level, the data do not provide sufficient evidence to conclude that the amount of television watched per day last year by the average person differed from that in 2005. (Note: x=4.752 hours and= s=2.384 hours.)

The confidence interval is

(Round to three decimal places as needed.)

According to a national study the average consumer unit spent $1739 on apparel and services in 2012. That same year, 25 consumer units in the Northeast were surveyed about their annual expenditures, in dollars, on apparel and services. At the 2% significance level, the data provide sufficient evidence to conclude that the 2012 mean annual expenditure on apparel and services for consumer units in the Northeast differed from the national mean of $1739. (Note: x=$1920.22 and s=$349.83.)

The confidence interval is

(Round 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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