Researchers often use z tests to compare their samples to known population norms. The Graded Naming Test (GNT) asks respondents to name objects in a set of 30 black-and-white drawings. The test, often used to detect brain damage, starts with easy words like kangaroo and gets progressively more difficult, ending with words like sextant. The GNT population norm for adults in England is 20.4. Roberts (2003) wondered whether a sample of Canadian adults had different scores than adults in England. If they were different, the English norms would not be valid for use in Canada. The mean for 30 Canadian adults was 17.5. For the purposes of this exercise, assume that the standard deviation of the adults in England is 3.2.
A. Conduct all six steps of a z test. Be sure to label all six steps.
B. Some words on the GNT are more commonly used in England. For example, a mitre, the headpiece worn by bishops, is worn by the archbishop of Canterbury in public ceremonies in England. No Canadian participant correctly responded to this item, whereas 55% of English adults correctly responded. Explain why we should be cautious about applying norms to people different from those on whom the test was normed.
C. When we conduct a one-tailed test instead of a two-tailed test, there are small changes in steps 2 and 4 of hypothesis testing. (Note: For this example, assume that those from populations other than the one on which it was normed will score lower, on average. That is, hypothesize that the Canadians will have a lower mean.) Conduct steps 2, 4, and 6 of hypothesis testing for a one-tailed test.
D. Under which circumstance—a one-tailed or a two-tailed test—is it easier to reject the null hypothesis? Explain.
E. If it becomes easier to reject the null hypothesis under one type of test (one-tailed versus two-tailed), does this mean that there is a bigger difference between the groups with a one-tailed test than with a two-tailed test? Explain.
F. When we change the p level that we use as a cutoff, there is a small change in step 4 of hypothesis testing. Although 0.05 is the most commonly used p level, other values, such as 0.01, are often used. For this example, conduct steps 4 and 6 of hypothesis testing for a two-tailed test and p level of 0.01, determining the cutoff and drawing the curve.
G. With which p level—0.05 or 0.01—is it easiest to reject the null hypothesis? Explain.
H. If it is easier to reject the null hypothesis with certain plevels, does this mean that there is a bigger difference between the samples with one p level versus the other plevel? Explain.
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Researchers often use z tests to compare their samples to known population norms. The Graded Naming...
1. What are null hypothesis and alternative hypothesis? 2. Inastatisticaltest,wehavethechoiceofatwo-tailedtest,aleft- tailed test, or a right-tailed test. Which hypothesis is the determining factor for choosing the direction of the test? (In other words, how would you decide it) 3. Forthesamesampledataandnullhypothesis,howdoesthe P-value for a two-tailed test compare to that for a one-tailed test? 4. Using P-value method, how would you reject or fail to reject the null hypothesis? (what is the decision criteria?) How does level of significance matter to the hypothesis...
When 40 people use the Weight Watchers diet for one year, their mean weight loss was 3.0 pounds. Historically the standard deviation is σ = 4.9 pounds (based on data from “Comparison of the Atkins, Ornish, Weight Watchers, and Zone Diets for Weight Loss and Heart Disease Reduction,” by Dansinger, et al., Journal of the American Medical Association, Vol. 293, No. 1). Use a 0.01 significance level to test the claim that the mean weight loss is greater than 0....
4) A researcher is testing a hypothesis of a single mean. The critical z value for α = .05 and a two tailed test is ±1.96. The observed z value from sample data is minus2.11. The decision made by the researcher based on this information is to _____ the null hypothesis. reject fail to reject redefine change the alternate hypothesis into restate 5) A researcher is testing a hypothesis of a single mean. The critical z value for α =...
3, Hypothesis testing for the mean (gis known) Find the P-value for a two-tailed hypothesis test with a standardized test statistic of z 1.64. Decide whether to reject Ho when the level of significance is α a. 0.10. b. Find the P-value for a right-tailed hypothesis test with a standardized test statistic of z 1.64. Decide whether to reject Ho when the level of significance is a0.10. Homeowners claim that the mean speed of automobiles traveling on their street is...
2. Hypothesis tests about a population mean, population standard deviation known Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the criteria lenders use to evaluate the creditworthiness of a potential borrower is her credit risk score, usually a FICO score. FICO scores range from 300 to 850. A consumer with a high FICO score is perceived to be a low credit risk to the lender and is more likely to be extended credit...
3. Hypothesis tests about a population mean, population standard deviation known Aa Aa Lenders tighten or loosen their standards for issuing credit as economic conditions change. One of the criteria lenders use to evaluate the creditworthiness of a potential borrower is his credit risk score, usually a FICO score. FICO scores range from 300 to 850. A consumer with a high FICO score is perceived to be a low credit risk to the lender and is more likely to be...
Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about μ = 28 ml/kg.† Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 31 24 43 35 32 36 31 The sample mean is x ≈ 33.1 ml/kg. Let x...
.0T IS Ubained WheR tésting the claim that p 0.345. 20. The test statistic of z-1.94 is obtained when testing the claim that p 3/8 two-tailed p value 0.524 Final Conclusions. In Exercises 25-28, use a significance level of a0.05 and use the given information for the following: a. State a conclusion about the null hypothesis. (Reject Ho or fail to reject Ho) b. Without using technical terms or symbols, state a final conclusion that addresses the original claim. 25....
Total blood volume (in ml) per body weight (in kg) is important in medical research. For healthy adults, the red blood cell volume mean is about μ = 28 ml/kg.† Red blood cell volume that is too low or too high can indicate a medical problem. Suppose that Roger has had seven blood tests, and the red blood cell volumes were as follows. 33 26 39 36 29 37 30 The sample mean is x ≈ 32.9 ml/kg. Let x...
Comparing Grocery Prices Consumer groups often analyze store prices and compare the price of similar items in different stores. They share this information with other consumers or customers. Imagine that a consumer group suspects that there is a difference in prices between two grocery stores (Store A and Store B). To investigate, the consumer group identifies the prices of six identical items at Stores A and B. Since prices change over time, the consumer group gathers all data on a...