What the range of the values of the test value which indicates that there is significant difference and that the null hypothesis should be rejected *?
Chapter 17. z-test for differences between means
1. Earphones and earplugs, Inc. wants to focus its marketing for a new compact disc player on young affluent professionals. Their marketing department identified two magazines, Wired Xers and Quiche & Volvo as being especially popular among their target population. 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. Formulate a pair of research and null hypotheses to test this claim. Show 2. Would you be doing a 1-tailed test or a 2-tailed test?
3. Determine the critical value for a 95% level of confidence (p<0.05).
4. Draw a normal curve, mark it with z values and ages, and shade the critical region. Because it is a 2-tailed test, either a positive or a negative difference will be relevant. 5.The advertising department of Wired Xers argued that, in fact, its readers were younger than those of Quiche & Volvo. Formulate the research and null hypotheses needed to test this contention. Then determine the critical region for a level of significance of p< 0.05. 6. Would you be doing a 1-tailed test or a 2-tailed test?
7. Determine the critical value for a 95% level of confidence (p<0.05).
8. Draw a normal curve, mark it with z values and ages, and shade the critical region.
9. A random sample of size 24 was selected from individual subscribers to Wired Xers. The ages were as follows:
A similar sample was drawn for Quiche & Volvo:
Calculate the means and standard deviations. To help, I’ve calculated some sums for you. I’ve used “W” for Wired Xers and “Q” for Quiche & Volvo.
10. Estimate the standard error of the mean for the population from which the Q&V sample was drawn. 11. Calculate the .95 and .99 confidence intervals about the mean for the Q&V sample.
12. 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. Use .05 as your probability level. Be careful here. Draw a normal curve and label it appropriately and shade the critical region. Don't be misled by the last two questions.
What is the range of test statistics indicating that the null hypothesis should be rejected?In null hypothesis testing, this criterion is called α (alpha) and is almost always set to . 05. If there is less than a 5% chance of a result as extreme as the sample result if the null hypothesis were true, then the null hypothesis is rejected.
What is the range of values for level of significance?The level of statistical significance is often expressed as a p-value between 0 and 1. The smaller the p-value, the stronger the evidence that you should reject the null hypothesis. A p-value less than 0.05 (typically ≤ 0.05) is statistically significant.
What value of at test is significant?We can work out the chances of the result we have obtained happening by chance. If a p-value reported from a t test is less than 0.05, then that result is said to be statistically significant. If a p-value is greater than 0.05, then the result is insignificant.
When the pThe smaller (closer to 0) the p-value, the stronger is the evidence against the null hypothesis. If the p-value is less than or equal to the specified significance level α, the null hypothesis is rejected; otherwise, the null hypothesis is not rejected.
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