The population variances are unknown and assumed to be unequal. The Welch–Satterthwaite approximation of the degrees of freedom for this test is 39.8360. Assume the conditions for a two‑sample ?t‑test are satisfied and calculate the ?‑statistic for this two‑sample ?t‑test. Compute the ?-value for the ?‑statistic using software. You may find one of these software manuals useful. Round your answers for both ?t and ? to two decimal places.
Many Americans believe that women talk more than men. A 1998 study tested this theory by evaluating the number of words spoken daily by men and women. The researcher of the study conducted a two-sample ?t‑test set at a signficance level of α=0.05. The null and alternative hypotheses, ?0 and ?1, are
where ?M represents the mean number of words spoken per day by men, and ?W represents the mean number of words spoken per day by women.
The researcher randomly selected 20 men and 27 women and tracked the number of words spoken per day by each individual over a period of time. The sample results are summarized in the table.
| Population | Sample size |
Sample mean (words) |
Sample standard deviation (words) |
|---|---|---|---|
| Men | ?M=20 | x¯M=12867 | ?M=8343 |
| Women | ?W= 27 | x¯W=16496 | ?W=7914 |
The population variances are unknown and assumed to be unequal. The Welch–Satterthwaite approximation of the degrees of freedom for this test is 39.8360.
Assume the conditions for a two‑sample ?t‑test are satisfied and calculate the ?‑statistic for this two‑sample ?t‑test. Compute the ?-value for the ?‑statistic using software. You may find one of these software manuals useful. Round your answers for both ?t and ? to two decimal places.
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