Answered: confidence interval leads to the same…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter2: The Integers

Section2.7: Introduction To Coding Theory (optional)

Problem 7E

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Listed below are the numbers of words spoken in a day by each member of eight different randomly selected couples. Complete parts (a) and (b) below.

Male	15,120	26,314	1464	7800	19,420	15,288	14,615	25,602
Female	24,185	13,795	18,744	17,195	12,673	17,157	16,456	18,185

a. Use a 0.01significance level to test the claim that among couples, males speak fewer words in a day than females.

In this example, μd is the mean value of the differences d for the population of all pairs of data, where each individual difference d is defined as the words spoken by the male minus words spoken by the female. What are the null and alternative hypotheses for the hypothesis test?

H0: μd [less than< equals= greater than> not equals≠] [] word(s)

H1: μd [less than< equals= not equals≠ greater than] [] word(s)

(Type integers or decimals. Do not round.)

Identify the test statistic: t=(Round to two decimal places as needed.)

Identify the P-value: P-value=(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test?

Since the P-value is (greater than/ less than or equal to) the significance level, (reject/ fail to reject) the null hypothesis. There (is/ is not)
sufficient evidence to support the claim that males speak fewer words in a day than females.

b. Construct the confidence interval that could be used for the hypothesis test described in part (a). What feature of the confidence interval leads to the same conclusion reached in part (a)?

The confidence interval is [ ]word(s)<μd<[ ] word(s). (Round to the nearest integer as needed.)

What feature of the confidence interval leads to the same conclusion reached in part (a)?

choose the best option in parentheses.

Since the confidence interval contains (only positive numbers, only negative numbers, zero) (reject, fail to reject) the null hypothesis.

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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