MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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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.
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