Question

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

Male   Female
28,318   19,830
17,170   23,071
3,896   4,269
29,439   18,574
24,265   12,044
8,740   14,884
19,875   11,237
16,529   19,452
26,558   13,036
21,742   19,734
10,094   16,432
12,281   13,765
10,927   17,777
19,776   23,963
18,776   5,567
2,082   16,597
21,459   22,032
10,191   18,234
18,738   14,988
15,314   13,702
14,995   28,030
19,158   8,367
7,914   18,943
6,664   5,057
27,001   10,509
9,688   18,386
15,390   13,872
10,622   20,049
13,030   21,233
19,201   10,978
15,115   35,478
9,674   7,658
19,043   12,493
16,434   12,009
10,575   31,573
13,180   21,329
13,954   18,208
11,507   18,798
17,784   21,930
12,311   15,108
12,233   20,054
6,682   13,927
19,005   17,720
14,573   14,614
17,019   30,798
14,648   37,737
19,598   26,085
38,253   33,865
18,184   23,480
47,564   29,711
24,907   18,903
11,216   7,219
15,087   24,810
9,229   14,862
6,288   13,057
20,368   26,728

a. Use a

0.050.05

significance level to test the claim that among​ couples, males speak fewer words in a day than females.In this​ example,

mu Subscript dμd

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?

Upper H 0H0​:

mu Subscript dμd

▼

greater than>

equals=

not equals≠

less than<

nothing ​word(s)

Upper H 1H1​:

mu Subscript dμd

▼

less than<

equals=

greater than>

not equals≠

nothing ​word(s)

​(Type integers or decimals. Do not​ round.)

Identify the test statistic.

tequals=nothing

​(Round to two decimal places as​ needed.)

Identify the​ P-value.

​P-valueequals=nothing

​(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

is

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

nothing

​word(s)less than<mu Subscript dμdless than<nothing

​word(s).

​(Round to one decimal place as​ needed.)

What feature of the confidence interval leads to the same conclusion reached in part​ (a)?

Since the confidence interval contains

▼

only positive numbers,

zero,

only negative numbers,

▼

fail to reject

reject

the null hypothesis.

Enter your answer in each of the answer boxes.

Answer 1