The difference between means will be calculated by subtracting the mean for W-Xers from the mean for Q&V so that, if the alternate hypothesis is true, the difference will be positive. 05 probability level, the critical value of z is 1.65. Don't be misled by the last two questions.īecause the hypotheses are directed (they make reference to the direction of the difference), you would do a 1-tailed test. Draw a normal curve and label it appropriately and shade the critical region. Can you conclude that the readers of Q&V are older than the readers of W-Xers? Determine whether the difference between the sample means is statistically significant. The 95% confidence interval will thus be 39.6250 ± 1.96 × 1.5798 or 39.6250 ± 3.0964 or 36.5286 to 42.7214.įor the 99% confidence interval, you multiply the standard error of the mean by 2.58 and then you subtract the result from the mean to get the lower limit and add the result to the mean to get the upper limit. 99 confidence intervals about the mean for the Q&V sample.įor the 95% confidence interval, you multiply the standard error of the mean by 1.96 and then you subtract the result from the mean to get the lower limit and add the result to the mean to get the upper limit. Estimate the standard error of the mean for the population from which the Q&V sample was drawn.ġ1. Ive used W for Wired Xers and Q for Quiche & Volvo.ġ0. To help, Ive calculated some sums for you. The ages were as follows:Ī similar sample was drawn for Quiche & Volvo:Ĭalculate the means and standard deviations. A random sample of size 24 was selected from individual subscribers to Wired Xers. The difference is calculated by subtracting the mean age of Wired Xers readers from the mean age of Quiche & Volvo readers because the null hypothesis says that readers of Wited Xers are younger than readers of Quiche & Volvo and, if the null hypothesis is true, the difference calculated this way will be positive.ĩ. Draw a normal curve, mark it with z values and ages, and shade the critical region. The critical value of z for this test will therefore be 1.65.Ĩ. For a 1-tailed test, you need a z greater than 1.65.
If you are using the 95% confidence level, for a 2-tailed test you need a z below -1.96 or above 1.96 before you say the difference is significant. Determine the critical value for a 95% level of confidence (p<0.05). Would you be doing a 1-tailed test or a 2-tailed test?īecause the hypotheses contain reference to the direction of the difference, this one involves a 1-tailed test.ħ. Then determine the critical region for a level of significance of p< 0.05.Ħ. Formulate the research and null hypotheses needed to test this contention. Draw a normal curve, mark it with z values and ages, and shade the critical region.īecause it is a 2-tailed test, either a positive or a negative difference will be relevant.ĥ.The advertising department of Wired Xers argued that, in fact, its readers were younger than those of Quiche & Volvo.
The critical value for a 95% two-tailed test is ± 1.96.Ĥ. Since the hypotheses are about the existence of a difference between the two means and not the direction of the difference, it would be a two-tailed test.ģ. Would you be doing a 1-tailed test or a 2-tailed test? Formulate a pair of research and null hypotheses to test this claim.Ģ. The advertising department of Quiche & Volvo claims that the age of its average subscriber is not the same as the average subscriber of Wired Xers. Their marketing department identified two magazines, Wired Xers and Quiche & Volvo as being especially popular among their target population.
wants to focus its marketing for a new compact disc player on young affluent professionals.