homework

What is the P-value? O the probability that the observed test statistic will take on values less extreme than the test statistic O the probability that the test statistic will take on values less extreme than the observed test statistic O the probability that the test statistic will take on values as extreme or more extreme than the observed test statistic Q) the probability that the observed test statistic will take on values as extreme or more extreme than the test statistic O the probability that the test statistic will take the value of the observed test statistic X In Chapters 8 and 9, you studied estimation and hypothesis testing. (a) What two sampling distributions are used in estimation and hypothesis testing of population means and proportions? (Select all that apply.) the standard normal distribution C] the standard f distribution C] the standard Student's distribution C] the Student's 2 distribution the Student's t distribution What are the criteria for determining the appropriate sampling distribution? [Select all that apply.) C] whether a mean (y) or proportion [p] is being considered [:1 known or unknown population sizes C] normality known or unknown 0 C] known or unknown degrees of freedom What assumptions will you make regarding population distributions? 0 that the population distributions are approximately uniform with known standard deviations C} that the population distributions are approximately normal with known standard deviations C} that the population distributions are approximately normal with unknown standard deviations {E that the population distributions are approximately normal with known means 0 that the population distributions are approximately uniform with unknown standard deviations X What graphics might be appropriate? (Select all that apply.) E] a regression line El a soatterplot E] a standard normal distribution showing the area(s] corresponding to the P-yalue a Student's tdistribution showing the areaEs) corresponding to the P-yalue a standard normal distribution Explain hypothesis testing to a friend, using the tollowmg scenario as a model, Descrioe the hypotheses, the sample statistic, the PWalIle, the meanings of Typel and Type [I errors, and the level or signicance. oiscuss the signicance of the results Formulas are not required. A team of research doctors designed a new knee surgery technique utilizing much smaller incisions than the standard method. They believe recovery times are shorter when the new method is used. Under the old method, the average recovery time for full use of the knee is p1 : 4.5 months. A random sample of 39 surgeries using the new method showed the average recovery time to he #2 s 3.5 months, with sample standard deviation of 1 5 months. The Dvalue for the test is 0.0003. The research team states that the results are statistically signicant at the 1% level of signicance. Descrioe the hypotheses, O Null hypothesis: the average recovery times are the same; Alternate hypothesis the avemge recovery time for the new method is not the same as the average recovery time for the old method 0 Null hypothesis: the average recovery time for the new method is less than the average recovery time for the old method; Alternate hypothesis: the average recovery times are the same 0 Null hypothesis: the average recovery times are the same; Alternate hypothesis the avemge recovery time for the new method is greater than the average recovery time forthe old method 0 Null hypothesis: the average recovery times are the same; Alternate hypothesis the avemge recovery time for the new method is less than the average recovery time for the old method What dues the Evalue mean? 0 It is the prohaoility that a sample could he gathered from the population with the given characteristics. 0 It is the probability that the population actually has that mean. 0 It is the probability that the sample has that mean. 0 It is the prohaoility that the population could have a sample like this again, what is the meaning of a Type I error? 0 Accept the hypothesis that the average recovery times are the same when in fact this is true. 0 Accept the hypothesis that the average recovery times are the same when in fact this is false. 0 Reject the hypothesis that the average recovery times are different when in fact this is true. 0 Reject the hypothesis that the average recovery times are different when in fact this is false. what is the meaning of a Type 11 error? 0 Accept the hypothesis that the average recovery times are the same when in fact this is true. 0 Accept the hypothesis that the average recovery times are the same when in fact this is false. 0 Reject the hypothesis that the average recovery times are different when in fact this is true. 0 Reject the hypothesis that the average recovery times are different when in fact this is false. what does it mean to be statistically signicant at the 1% level of signicance? 0 That the psvalue is less than the 1% level that we are testing it against, allowing us to accept the alternate hypothesis 0 That the p-value is greater than the 1% level that we are testing it against, allowing us to fail to reject the null hypothesis. 0 That the Prvaiue is less than the 1% level that we are testing it against, allowing us to reject the null hypothesis 0 That the P-vaiue is greater than the 1% level that we are testing it against, allowing us to reject the null hypothesis. 0 That the Prvaiue is less than the 1% level that we are testing it against, allowing us to fall to reject the null hypothesis. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories? O Since the P-value > a, we fail to reject the null hypothesis. Since the P-value > a, we reject the null hypothesis. O Since the P-value s a, we reject the null hypothesis. O Since the P-value s a, we fail to reject the null hypothesis. (e) Interpret your conclusion in the context of the application. O At the 5% level of significance, the evidence is insufficient to conclude that current fish distribution is different than that of five years ago. O At the 5% level of significance, the evidence is sufficient to conclude that current fish distribution is different than that of five years ago.\fThe following table shows the Myers-Briggs personality preferences for a random sample of 406 people in the listed professions. E refers to extroverted and I refers to introverted. Person T e Occupation E I RowTotal Clergy [all denominations) 63 44 10? MD. 72 90 152 Lawyer 51 86 137 Column Total H6 220 406 Use the chi-square test to determine if the listed occupations and personality preferences are independent at the 0.05 level of signicance. (3) What is the level of signicance? State the null and alternate hypotheses. O HU: MyersVBIiggs preference and profession are not independent H1: Myers-Briggs preference and profession are not independent. 0 HO: MyersrBIiggs preference and profession are independent H1: Myers-Briggs preference and profession are independent. 0 HO: MyersrBIiggs preference and profession are independent H1: Myers-Briggs preference and profession are not independent. 0 HO: MyersVBriggs preference and profession are not independent H1: MyersVBriggs preference and profession are independent. (b) Find the value of the chiisquare statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.) : Are all the expected frequencies greater than 5? 0 Yes 0 No What sampling distribution will you use'.J O chi-square O binomial O uniform 0 normal 0 Student's b What are the degrees of freedom? The Fish and Game Department stocked a lake with fish in the following proportions: 30% catfish, 15% bass, 40% bluegill, and 15% pike. Five years later it sampled the lake to see if the distribution of fish had changed. It found that the 500 fish in the sample were distributed as follows. Catfish Bass Bluegill Pike 116 87 218 79 In the 5-year interval, did the distribution of fish change at the 0.05 level? (a) What is the level of significance? State the null and alternate hypotheses. O Ho: The distributions are the same. H, : The distributions are the same. O Ho: The distributions are the same. H,: The distributions are different. O Ho: The distributions are different. H, : The distributions are different. O Ho: The distributions are different. H1 : The distributions are the same. (b) Find the value of the chi-square statistic for the sample. Are all the expected frequencies greater than 5? Yes O No What sampling distribution will you use? O uniform O Student's t O chi-square O normal O binomial What are the degrees of freedom? (c) Estimate the P-value of the sample test statistic. O P-value > 0.100 O 0.050