The accompanying table lists the numbers of words spoken in a day by each member of 56 different randomly selected couples. Complete parts (a) and (b) below. The chart to view the data on words spoken in a day by the couples is below a. Use a 0.05significance 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 ? _word(s) H1: μd ? _ 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 the significance level, reject or fail to reject the null hypothesis. There is or 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 one decimal place as needed.) Words Spoken In A Day Male Female 27,548 21,889 14,349 26,172 3,946 6,480 26,473 18,365 26,801 11,142 7,444 16,904 20,418 10,069 15,712 18,963 25,497 12,477 23,895 20,609 13,483 15,101 9,328 13,025 14,420 15,856 23,274 23,198 17,259 7,129 2,163 18,564 22,187 22,242 8,552 17,929 19,028 17,607 18,341 11,928 15,656 31,573 19,146 8,899 6,957 15,963 5,870 3,842

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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The accompanying table lists the numbers of words spoken in a day by each member of

56 different randomly selected couples. Complete parts (a) and (b) below.

The chart to view the data on words spoken in a day by the couples is below

a. Use a 0.05significance 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 ? ___word(s)

H1: μd ? ___ word(s)

(Type integers or decimals. Do not round.)

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 the significance level,

reject or fail to reject

the null hypothesis. There

is or 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 one decimal place as needed.)

Words Spoken In A Day

Male	Female
27,548	21,889
14,349	26,172
3,946	6,480
26,473	18,365
26,801	11,142
7,444	16,904
20,418	10,069
15,712	18,963
25,497	12,477
23,895	20,609
13,483	15,101
9,328	13,025
14,420	15,856
23,274	23,198
17,259	7,129
2,163	18,564
22,187	22,242
8,552	17,929
19,028	17,607
18,341	11,928
15,656	31,573
19,146	8,899
6,957	15,963
5,870	3,842

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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