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 15,919 26,768 1447 7766 18,809 15,044 13,710 26,576 Female 24,862 13,288 18,663 17,711 12,702 17,351 16,162 18,175 a. Use a 0.05 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 ▼ not equals≠ greater than> less than< equals= _____ word(s) H1: μd ▼ less than< equals= greater than> not equals≠ _____ 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)? Since the confidence interval contains ▼ zero, only negative numbers, only positive numbers, ▼ reject fail to reject the null hypothesis.

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 15,919 26,768 1447 7766 18,809 15,044 13,710 26,576 Female 24,862 13,288 18,663 17,711 12,702 17,351 16,162 18,175 a. Use a 0.05 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 ▼ not equals≠ greater than> less than< equals= ___ word(s) H1: μd ▼ less than< equals= greater than> not equals≠ _ 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)? Since the confidence interval contains ▼ zero, only negative numbers, only positive numbers, ▼ reject fail to 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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Question

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	15,919	26,768	1447	7766	18,809	15,044	13,710	26,576
Female	24,862	13,288	18,663	17,711	12,702	17,351	16,162	18,175

a. Use a 0.05 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

▼

not equals≠

greater than>

less than<

equals=

_____ word(s)

H1:

μd

▼

less than<

equals=

greater than>

not equals≠

_____ 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 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)?

Since the confidence interval contains

▼

zero,

only negative numbers,

only positive numbers,

▼

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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