A recent study focused on the number of times men and women who live alone buy take-out dinner in a month. Assume that the distributions follow the normal probability distribution and the population standard deviations are equal. The information is summarized below.
Statistic | Men | Women |
Sample mean | 25.45 | 22.04 |
Sample standard deviation | 5.91 | 4.68 |
Sample size | 37 | 40 |
At the 0.01 significance level, is there a difference in the mean number of times men and women order take-out dinners in a month?
State the decision rule for 0.01 significance level: H_{0}: μ_{Men}= μ_{Women} H_{1}: μ_{Men} ≠ μ_{Women.} (Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.)
Compute the value of the test statistic. (Round your answer to 3 decimal places.)
What is your decision regarding the null hypothesis?
What is the p-value? (Round your answer to 3 decimal places.)
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