been made? What could you do to reduce the chance of that type of error?
- If The Decision In 1 1 3 Is Actually Unknown To Us Incorrect What Type Of Error Has Been Made What Could You Do 1 (160.47 KiB) Viewed 468 times
If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has been made? What could you do
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If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has been made? What could you do
If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has
been made? What could you do to reduce the chance of that type of error?
1.1 An extract of a study conducted about the effects of a special class designed to aid students with verbal skills is given below: Each child was given a verbal skill test twice, both before and after completing a 4-week period in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population mean μ for Y is equal to 0, the class has no effect, on the average. For the four children in the study, the observed values of Y are 8-5-3, 10-3-7, 5-2-3, and 7-4-3 (e.g. for the first child, the scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5-3). It is planned to test the null hypothesis of no effect against the alternative hypothesis that the effect is positive, based on the following results from a statistical software package: Variable Number of cases Mean Standard Deviation Standard Error Y 4 4.000 2.000 1.000 1.1.1 Set up the null and alternative hypotheses. (4) 1.1.2 Calculate the test statistic, and indicate whether the P-value was below 0.05, based on using the appropriate table. (7) (4) 1.1.3 Make a decision, using a = .05. Interpret. 1.1.4 If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has been made? What could you do to reduce the chance of that type of error? (3) 1.1.5 True or false? When we make a decision using a = .05, this means that if the special class is truly beneficial, there is only a 5% chance that we will conclude that it is not beneficial. (3) 1.2 For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 non-vegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students. 1.2.1 Defining appropriate notation, state the null and alternative hypotheses for testing whether there is a difference between population mean ideology for vegetarian and non- vegetarian students. (4) 1.3 When we use statistical software to compare the means with a significance test, we obtain the following printout: Variance T DF Prob>T Unequal 2.9146 41.9 0.006 1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked to make a decision at some a-level.) (5) QUESTION TWO (30 MARKS) 2.1 A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let u be true mean weight of individuals before starting the diet and let u be the true mean weight of individuals after 3 weeks on the diet. 1 2 3 4 5 Weight before diet 156 201 194 203 210 Weight after diet 149 196 191 197 206 Given that Sa -1.58, test to determine if the diet is effective at reducing weight. Use a=0.1 (20)
been made? What could you do to reduce the chance of that type of error?
1.1 An extract of a study conducted about the effects of a special class designed to aid students with verbal skills is given below: Each child was given a verbal skill test twice, both before and after completing a 4-week period in the class. Let Y = score on exam at time 2 - score on exam at time 1. Hence, if the population mean μ for Y is equal to 0, the class has no effect, on the average. For the four children in the study, the observed values of Y are 8-5-3, 10-3-7, 5-2-3, and 7-4-3 (e.g. for the first child, the scores were 5 on exam 1 and 8 on exam 2, so Y = 8-5-3). It is planned to test the null hypothesis of no effect against the alternative hypothesis that the effect is positive, based on the following results from a statistical software package: Variable Number of cases Mean Standard Deviation Standard Error Y 4 4.000 2.000 1.000 1.1.1 Set up the null and alternative hypotheses. (4) 1.1.2 Calculate the test statistic, and indicate whether the P-value was below 0.05, based on using the appropriate table. (7) (4) 1.1.3 Make a decision, using a = .05. Interpret. 1.1.4 If the decision in (1.1.3.) is actually (unknown to us) incorrect, what type of error has been made? What could you do to reduce the chance of that type of error? (3) 1.1.5 True or false? When we make a decision using a = .05, this means that if the special class is truly beneficial, there is only a 5% chance that we will conclude that it is not beneficial. (3) 1.2 For a random sample of Harvard University psychology majors, the responses on political ideology had a mean of 3.18 and standard deviation of 1.72 for 51 non-vegetarian students and a mean of 2.22 and standard deviation of .67 for the 20 vegetarian students. 1.2.1 Defining appropriate notation, state the null and alternative hypotheses for testing whether there is a difference between population mean ideology for vegetarian and non- vegetarian students. (4) 1.3 When we use statistical software to compare the means with a significance test, we obtain the following printout: Variance T DF Prob>T Unequal 2.9146 41.9 0.006 1.3.1 Interpret the P-value, in context, based on its definition. (Note: You are not being asked to make a decision at some a-level.) (5) QUESTION TWO (30 MARKS) 2.1 A new weight-reducing technique, consisting of a liquid protein diet, is currently undergoing tests by the Food and Drug Administration (FDA) before its introduction into the market. The weights of a random sample of five people are recorded before they are introduced to the liquid protein diet. The five individuals are then instructed to follow the liquid protein diet for 3 weeks. At the end of this period, their weights (in pounds) are again recorded. The results are listed in the table. Let u be true mean weight of individuals before starting the diet and let u be the true mean weight of individuals after 3 weeks on the diet. 1 2 3 4 5 Weight before diet 156 201 194 203 210 Weight after diet 149 196 191 197 206 Given that Sa -1.58, test to determine if the diet is effective at reducing weight. Use a=0.1 (20)
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