In a sample of 186 men, the mean number of words spoken in a day is XXXXXXXXXXwith a standard deviation of XXXXXXXXXXwords. In a sample of 217 women, the mean number of words spoken in a day is...

In a sample of 186 men, the mean number of words spoken in a day is 15657.9 with a standard deviation of 8659.4 words. In a sample of 217 women, the mean number of words spoken in a day is 16209.3 with a standard deviation of 7294.1 words. Use a 0.01 significance level to test the claim that the mean number of words spoken in a day by men is less than that for women.

If we let:

Let μ
₁be the population mean number of words spoken in a day by men, and μ
₂be the population mean number of words spoken in a day by women.

Letp₁be the population proportion of words spoken in a day by men, andp₂be the population proportion of words spoken in a day by women.

Round to three decimal places if necessary.

a)

    Null hypothesis H₀ :  .

    Alternate hypothesis H₁ :  .

b) Type of test:  -tailed test.

c) significance level: α =

d) Test statistic:

e) Compute p-value of the test statistic.

f)  Decision: