Two samples each of size 25 are taken from independent populations assumed to be

Question

Two samples each of size 25 are taken from independent populations assumed to be normally distributed with equal variances. The first sample has a mean of 35.5 and standard deviation of 3.0 while the second sample has a mean of 33.0 and standard deviation of 4.0. Which of the following statement is correct? To test the null hypothesis of no difference in the population means at the alpha = 0.05 level, the critical value is plusminus 1.96. The p-value for a one-tail test in the hypothesized direction is between 0.01 and 0.05 The null hypothesis of no difference in the population means would not be rejected at the alpha = 0.05 level of significance. The 99% confidence interval estimate for the difference in the two means include 0.

Explanation / Answer

`+try to find out the 99% equal tailed confidence interval of the differnce of the two population means:

this is equal to: (35.5-33.0)+/-2.5758{9/25+16/25}^(1/2)=(-.5758,5.0758)

We can see it contains 0, hence option 4

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