In a study to investigate whether women are really more talkative than men, the difference in the numbers of words spoken in a day by the male (male;) and female (female;) members of 56 randomly selected couples (di male, female,, i = 1, 2, ..., 56) was recorded and the following summary statistics were produced: = 56 56 Σdi –104,558, Σα = = 4, 605, 935, 512. i=1 i=1 (a) Calculate the sample mean and the sample variance for the differences. (b) State the null and alternative hypotheses for a paired t-test. (c) Show that the test statistic is t = -1.56 and hence determine whether the null hypothesis can be rejected at the 5% significance level. =

MATLAB: An Introduction with Applications
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In a study to investigate whether women are really more talkative than men, the difference
in the numbers of words spoken in a day by the male (male;) and female (female;) members
of 56 randomly selected couples (d; = male; — female;, i = 1, 2, ..., 56) was recorded and
the following summary statistics were produced:
56
56
Σ di = -104,558, Σd = 4,605,935,512.
i=1
i=1
(a) Calculate the sample mean and the sample variance for the differences.
(b) State the null and alternative hypotheses for a paired t-test.
=
(c) Show that the test statistic is t -1.56 and hence determine whether the null
hypothesis can be rejected at the 5% significance level.
Transcribed Image Text:In a study to investigate whether women are really more talkative than men, the difference in the numbers of words spoken in a day by the male (male;) and female (female;) members of 56 randomly selected couples (d; = male; — female;, i = 1, 2, ..., 56) was recorded and the following summary statistics were produced: 56 56 Σ di = -104,558, Σd = 4,605,935,512. i=1 i=1 (a) Calculate the sample mean and the sample variance for the differences. (b) State the null and alternative hypotheses for a paired t-test. = (c) Show that the test statistic is t -1.56 and hence determine whether the null hypothesis can be rejected at the 5% significance level.
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