1、Tests of Significance: The Basics,BPS chapter 15, 2006 W.H. Freeman and Company,Statistical significance,A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary sligh
2、tly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.What is the size of the observed effect?3.68 oz. -3.68 oz. 4 3.6
3、8 = 0.32 oz. 3.68 4 = - 0.32 oz.,Statistical significance (answer),A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects
4、that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.What is the size of the observed effect?3.68 oz. -3.68 oz. 4 3.68 = 0.32 oz. 3.68 4 = - 0.32 oz.,Stati
5、stical significance,A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less
6、 than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.The consumer advocate should declare statistical significance only if there is a small probability ofObserving a sample mean of 3.68 oz. or less when
7、 = 4 oz. Observing a sample mean of exactly 3.68 oz. when = 4 oz. Observing a sample mean of 3.68 oz. or greater when = 4 oz. Observing a sample mean of less than 4 oz. when = 4 oz.,Statistical significance (answer),A consumer advocate is interested in evaluating the claim that a new granola cereal
8、contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calc
9、ulates a sample mean of 3.68 ounces of cashews.The consumer advocate should declare statistical significance only if there is a small probability ofObserving a sample mean of 3.68 oz. or less when = 4 oz. Observing a sample mean of exactly 3.68 oz. when = 4 oz. Observing a sample mean of 3.68 oz. or
10、 greater when = 4 oz. Observing a sample mean of less than 4 oz. when = 4 oz.,Statistical significance,A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightl
11、y from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.Suppose the consumer advocate computes the probability described i
12、n the previous question to be 0.0048. Her result is Statistically significant. Not statistically significant.,Statistical significance (answer),A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes tha
13、t the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.Suppose the consumer advo
14、cate computes the probability described in the previous question to be 0.0048. Her result is Statistically significant. Not statistically significant.,Statistical significance,A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every b
15、ag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of c
16、ashews.If the probability described in the previous question is 0.0048, the difference between the observed value and the hypothesized value is Small. Large.,Statistical significance (answer),A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of ca
17、shews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of
18、3.68 ounces of cashews.If the probability described in the previous question is 0.0048, the difference between the observed value and the hypothesized value is Small. Large.,Statistical significance,A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounce
19、s of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample m
20、ean of 3.68 ounces of cashews.If the probability described in the previous question is 0.0048, then the consumer advocate should conclude that the granola is Correctly labeled. Incorrectly labeled.,Statistical significance (answer),A consumer advocate is interested in evaluating the claim that a new
21、 granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of
22、 cereal and calculates a sample mean of 3.68 ounces of cashews.If the probability described in the previous question is 0.0048, then the consumer advocate should conclude that the granola is Correctly labeled. Incorrectly labeled.,Stating hypotheses,A consumer advocate is interested in evaluating th
23、e claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocate recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sa
24、mple of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.What alternative hypothesis does she want to test?,Stating hypotheses (answer),A consumer advocate is interested in evaluating the claim that a new granola cereal contains “4 ounces of cashews in every bag.” The advocat
25、e recognizes that the amount of cashews will vary slightly from bag to bag, but she suspects that the mean amount of cashews per bag is less than 4 ounces. To check the claim, the advocate purchases a random sample of 40 bags of cereal and calculates a sample mean of 3.68 ounces of cashews.What alte
26、rnative hypothesis does she want to test?,Statistical significance,We reject the null hypothesis wheneverP-value . P-value . P-value . P-value .,Statistical significance (answer),We reject the null hypothesis wheneverP-value . P-value . P-value . P-value .,Statistical significance,The significance l
27、evel is denoted byP-value,Statistical significance (answer),The significance level is denoted byP-value,Statistical significance,Which of the following is a conservative choice for significance level?0 0.01 0.25 0.50 0.75 1,Statistical significance (answer),Which of the following is a conservative c
28、hoice for significance level?0 0.01 0.25 0.50 0.75 1,Calculating P-values,To calculate the P-value for a significance test, we need to use information about theSample distribution Population distribution Sampling distribution of,Calculating P-values (answer),To calculate the P-value for a significan
29、ce test, we need to use information about theSample distribution Population distribution Sampling distribution of,Conclusions,Suppose the P-value for a hypothesis test is 0.304. Using = 0.05, what is the appropriate conclusion?Reject the null hypothesis. Reject the alternative hypothesis. Do not rej
30、ect the null hypothesis. Do not reject the alternative hypothesis.,Conclusions (answer),Suppose the P-value for a hypothesis test is 0.304. Using = 0.05, what is the appropriate conclusion?Reject the null hypothesis. Reject the alternative hypothesis. Do not reject the null hypothesis. Do not reject
31、 the alternative hypothesis.,Conclusions,Suppose the P-value for a hypothesis test is 0.0304. Using = 0.05, what is the appropriate conclusion?Reject the null hypothesis. Reject the alternative hypothesis. Do not reject the null hypothesis. Do not reject the alternative hypothesis.,Conclusions (answ
32、er),Suppose the P-value for a hypothesis test is 0.0304. Using = 0.05, what is the appropriate conclusion?Reject the null hypothesis. Reject the alternative hypothesis. Do not reject the null hypothesis. Do not reject the alternative hypothesis.,P-value,True or False: The P-value should be calculate
33、d BEFORE choosing the significance level for the test.True False,P-value (answer),True or False: The P-value should be calculated BEFORE choosing the significance level for the test.True False,Conclusions,Suppose a significance test is being conducted using a significance level of 0.10. If a student
34、 calculates a P-value of 1.9, the studentShould reject the null hypothesis. Should fail to reject the null hypothesis. Made a mistake in calculating the P-value.,Conclusions (answer),Suppose a significance test is being conducted using a significance level of 0.10. If a student calculates a P-value
35、of 1.9, the studentShould reject the null hypothesis. Should fail to reject the null hypothesis. Made a mistake in calculating the P-value.,Stating hypotheses,If we test H0: = 40 vs. Ha: 40, this test is One-sided (left tail). One-sided (right tail). Two-sided.,Stating hypotheses (answer),If we test
36、 H0: = 40 vs. Ha: 40, this test is One-sided (left tail). One-sided (right tail). Two-sided.,Stating hypotheses,If we test H0: = 40 vs. Ha: 40, this test is One-sided (left tail). One-sided (right tail). Two-sided.,Stating hypotheses (answer),If we test H0: = 40 vs. Ha: 40, this test is One-sided (l
37、eft tail). One-sided (right tail). Two-sided.,Using CIs to test,A researcher is interested in estimating the mean yield (in bushels per acre) of a variety of corn. From her sample, she calculates the following 95% confidence interval: (118.74, 128.86). Her colleague wants to test (at = 0.05) whether
38、 or not the mean yield for the population is different from 120 bushels per acre. Based on the given confidence interval, what can the colleague conclude?The mean yield is different from 120 and it is statistically significant. The mean yield is not different from 120 and it is statistically signifi
39、cant. The mean yield is different from 120 and it is not statistically significant. The mean yield is not different from 120 and it is not statistically significant.,Using CIs to test (answer),A researcher is interested in estimating the mean yield (in bushels per acre) of a variety of corn. From he
40、r sample, she calculates the following 95% confidence interval: (118.74, 128.86). Her colleague wants to test (at = 0.05) whether or not the mean yield for the population is different from 120 bushels per acre. Based on the given confidence interval, what can the colleague conclude?The mean yield is different from 120 and it is statistically significant. The mean yield is not different from 120 and it is statistically significant. The mean yield is different from 120 and it is not statistically significant. The mean yield is not different from 120 and it is not statistically significant.,
