Confidence intervals!!!

Question

A publishing company wanted to test whether typing speed differs when using word processor A or word processor B. A random sample of 25 typists was selected and the typing speeds (in words per minute) were recorded for each secretary when using word processor A and then when using word processor B. (Which word processor was used first was determined for each typist by a coin flip).

Based on the collected data, a 95% confidence interval for μ_d, the mean difference (word processor A - word processor B) was found to be (2.5, 7.8).

The appropriate hypotheses for testing whether the typing speeds differ when using word processor A or word processor B is the two-sided test:

 

 

Based on this confidence interval for μ_d, what would be your conclusion (at the .05 significance level)? Explain.

This is an open ended question. 

Answer 1

The 95% confidence level corresponds to a level of significance = 0.05 for a two sided test.

Based on the confidence interval, we are 95% confident the plausible values for the difference of the population means is between 2.5 and 7.8.

Since those values do not include zero, we would conclude the population means differ at a 0.05 level of significance.