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 15,071 25,527 1461 8061 18,248 15,565 13,845 25,042 Female 24,849 13,483 18,874 18,503 12,530 17,604 15,855 19,353 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? H0: μd ▼ greater than> not equals≠ equals= less than< nothing word(s) H1: μd ▼ less than< equals= greater than> not equals≠ nothing word(s) (Type integers or decimals. Do not round.) Identify the test statistic. t=negative (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,k less than or equal to the significance level, fail to reject or 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 negative ???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)? Since the confidence interval contains --- fail to reject or reject the null hypothesis.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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	15,071	25,527	1461	8061	18,248	15,565	13,845	25,042
Female	24,849	13,483	18,874	18,503	12,530	17,604	15,855	19,353

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?

H0:

μd

▼

greater than>

not equals≠

equals=

less than<

nothing

word(s)

H1:

μd

▼

less than<

equals=

greater than>

not equals≠

nothing

word(s)

(Type integers or decimals. Do not round.)

Identify the test statistic.

t=negative

(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,k less than or equal to

the significance level,

fail to reject or 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

negative ???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)?

Since the confidence interval contains ---

fail to reject or 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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