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 15,495 27,251 1357 7741 18,280 15,583 13,978 25,901 Female 24,768 13,676 17,908 17,382 12,596 17,411 16,693 19,336 a. Use a 0.01 significance 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? 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 the significance level, fails to reject the null hypothesis. There 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.)

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

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter0: Preparing For Algebra

Section0.11: Simple Probability And Odds

Problem 13E

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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	15,495	27,251	1357	7741	18,280	15,583	13,978	25,901
Female	24,768	13,676	17,908	17,382	12,596	17,411	16,693	19,336

a. Use a 0.01 significance 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?

Identify the test statistic.

(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

the significance level, fails to reject

the null hypothesis. There 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.)

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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