55 Do men take a different amount of time than women to get out of bed in the morning? The 59 men observed averaged 6.7 minutes to get out of bed after the alarm rang. Their standard deviation was 2.2. The 49 women observed averaged 6 minutes and their standard deviation was 1.8 minutes. What can be concluded at the o = 0.01 level of significance? a. For this study, we should use Select an answer v b. The null and alternative hypotheses would be: Ho: Select an answer v| Select an answer v Select an answer v (please enter a decimal) H1: Select an answer v Select an answer v Select an answer v (Please enter a decimal) c. The test statistic ? v = (please show your answer to 3 decimal places.) d. The p-value = (Please show your answer to 4 decimal places.) e. The p-value is ? v a f. Based on this, we should Select an answer v the null hypothesis. g. Thus, the final conclusion is that ... The results are statistically significant at o = 0.01, so there is sufficient evidence to conclude that the population mean time for men to get out of bed in the morning is different than the population mean time for women to get out of bed in the morning. The results are statistically significant at o = 0.01, so there is sufficient evidence to conclude that the mean time to get out of bed in the morning for the 59 men that were observed is different than the mean time for the 49 women that were observed. The results are statistically insignificant at o = 0.01, so there is insufficient evidence to conclude that the population mean time for men to get out of bed in the morning is different than the population mean time for women to get out of bed in the morning. The results are statistically insignificant at o = 0.01, so there is statistically significant evidence to conclude that the population mean time for men to get out of bed in the morning is equal to the population mean time for women to get out of bed in the morning. h. Interpret the p-value in the context of the study. If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 59 men and 49 women are observed then there would be a 7.18% chance that the mean time to get out of bed in the morning for the 59 men would differ from the mean time to get out of bed in the morning for the 49 women by at least 0.7 minutes. O There is a 7.18% chance that the mean time to get out of bed in the morning for the 59 men differs by at least 0.7 minutes from the mean time to get out of bed in the morning for the 49 women. O There is a 7.18% chance of a Type | error. If the sample mean time to get out of bed in the morning for the 59 men is the same as the sample mean time to get out of bed in the morning for the 49 women and if another 59 men and 49 women are observed then there would be a 7.18% chance of concluding that the mean time to get out of bed in the morning for the 59 men differs by at least 0.7 minutes from the mean time to get out of bed in the morning for the 49 women i. Interpret the level of significance in the context of the study. If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 59 men and 49 women are observed then there would be a 1% chance that we would end up falsely concluding that the sample mean time for these 59 men and 49 women to get out of bed in the morning differ from each other. O There is a 1% chance you will take so long to get out of bed in the morning that you will miss the deadline to complete this assignment. O If the population mean time for men to get out of bed in the morning is the same as the population mean time for women to get out of bed in the morning and if another 59 men and 49 women are observed then there would be a 1% chance that we would end up falsely concluding that the population mean time for men to get out of bed in the morning is different than the population mean time for women to get out of bed in the morning There is a 1% chance that there is a difference in the population mean time for men and women to get out of bed in the morning.5? :- A report just came out that stated that 24.1% of all Americans say that vanilla is their favorite ice cream, 21. .\" sar,r that chocolate is their favorite, 9.1% favor butter pecan, 3.9% favor strawberry, and the rest have other favorites. An ice cream shop owner thinks that her customers are not like the rest of .-merica. The table belov.I shows the results of 94'] of her patrons' ice cream selections. What can be concluded at the o: = 13.10 significance level? a. Complete the table by filling in the expected frequencies. Round your answers to the nearest whole number: Frequencies of Favorite Ice Cream Expected Frequenw \"I:- -l:- \"I:- \"I:- b. What is the correct statistical test to use? Seleol an answer V c. What are the null and alternative hvpotheses? Hg: C Favorite ice cream and where the ice cream is purchased are independent. C The distribution of favorite ice cream for customers at her shop is not the same as it is for Americ ans in general. '33 Favorite ice cream and where the ice cream is purchased are dependent. \".3 The distribution of favorite ice cream for customers at her shop is the same as it is for Americ ans in general. H]: '33 The distribution of favorite ice cream for customers at her shop is the same as it is for Amec ans in general. C Favorite ice cream and where the ice cream is purchased are dependent. \".3 Favorite ice cream and where the ice cream is purchased are independent. C The distribution of favorite ice cream for customers at her shop is not the same as it is for Americ ans in general. d. The degrees of freedom = I I e. The test-statistic for this data =I I [Please shov.I your answer to three decimal places.} f. The p-value for this sample =I IfF'lease show your answer to four decimal places.} a- The p-value is a h. Based on this, we should i. Thus, the final conclusion is... '33 There is sufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. '33 There is sufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is the same as it is forAmericans in general. C There is insufficient evidence to conclude that favorite ice cream and where the ice cream is purchased are dependent. ".3 There is insufficient evidence to conclude that the distribution of favorite ice cream for customers at her shop is not the same as it is for Americans in general. C There is sufficient evidence to conclude that favorite ice cream and where the ice cream is purchased are dependent. 58 v A fisherman is interested in whether the distribution of fish caught in Green Valley Lake is the same as the distribution of fish caught in Echo Lake. Of the 330 randomly selected fish caught in Green Valley Lake, 131 were rainbow trout, 62 were other trout, 5? were bass, and 30 were catfish. Of the 495 randomly selected fish caught in Echo Lake, 21? were rainbow trout, 123 were other trout, 80 were bass, and m were catfish. Conduct the appropriate hypothesis test using an a = [LEI] level of significance. a. What is the correct statistical test to use? Goodness-of-Fit Independence Homogeneity Paired ttest X o" b. Ehat are the null and alternative hypotheses? ['1 Fish breed and lake are independent. The distribution of fish is not the same for Green Valley Lake and Echo Lake. The distribution of fish is the same for Green Valley Lake and Echo Lake. Fish breed and lake are dependent. 59 Here is a bivariate data set. X y 39 22 47 108 60 41 95 - 122 80 67 76 77 -0 81 -26 92 -128 Find the correlation coefficient and report it accurate to four decimal places. r = -0.74 X63 v