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 μd, 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:H_0: μ_d = 0, H_a: μ_d ≠ 0Based on this confidence interval for μd, what would be your conclusion (at the .05 significance level)? Explain.

Answer 1

Decision: Reject the null hypothesis.

Explanation:

Hello!

To test whether the typing speed differs when using word processor A or B a random sample of 25 typists was taken, they first used the word processor A and their times were recorded. Then they used the word processor B and their times were recorded. With the information obtained the variable difference Xd: Xa -Xb was determined. (This is a paired sample case)

Using the data the Confidence Interval at 95% level for the population mean μd was made

[2.5; 7.8] words per minute.

To know if there is any difference between processors, the company stated the hypothesis:

H₀: μd = 0

H₁: μd ≠ 0

α: 0.05

Remember, to decide a hypothesis test using a confidence interval, the following conditions should be met:

• The study parameter should be the same for the hypothesis and the confidence interval.
• The hypothesis test should be two-tailed.
• The confidence level of the interval and the significance level of the hypothesis test should be complementary. (if 1-α: 0.95 for the CI then α: 0.05 for the test)

If these conditions are met, you can decide using the confidence interval using the decision rule:

If the interval contains the 0, then you do not reject the null hypothesis.

If the interval doesn't contain the 0, then you reject the null hypothesis.

Since your interval doesn't contain the 0, the decision should be to reject the null hypothesis. In other words, there is enough statistical evidence to say that the population mean of the difference between the typing speed while using the word processor A and the typing speed while using the word processor B is not cero. One of the word processors allows a faster typing speed.

Since the variable Xd was constructed using the data from "A" minus the data from "B", and taking into consideration that both bonds of the confidence interval are positive, it is possible that the typing speed obtained using the word processor A is faster than the speed with word processor B. However this is just a supposition, to be certain a new hypothesis test is needed.

I hope this helps!