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 |
16,044 |
26,686 |
1433 |
7813 |
19,439 |
15,672 |
14,187 |
25,068 |
Female |
24,753 |
13,006 |
18,419 |
18,015 |
13,045 |
17,349 |
16,311 |
17,984 |
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, 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
null and alternative hypotheses for the hypothesis test?
: ____ word(s)
: ____ 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, ____ the null hypothesis. There ____ 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) < < ____ 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 ____ ____ the null hypothesis.