1. Can a pretest on mathematics skills predict success in a statistics course? The 82 students in an introductory statistics class took a pretest at the beginning of the semester. The least-squares regression line for predicting the score y on the final exam from the pretest score x was = 9.8 + 0.76x. The standard error of b1 was 0.44. (a) Test the null hypothesis that there is no linear relationship between the pretest score and the score on the final exam against the two-sided alternative. (Round your test statistic to three decimal places and your P-value to four decimal places.) RN_3878578_8_ t= {"js_version":0} RN_3878578_8_ df = {"js_version":0} RN_3878578_8_ P= {"js_version":0} Conclusion mc We reject H0 at the 5% significance level. We do not reject H0 at the 5% significance level. RC_3878578_8_3 {} (b) Would you reject this null hypothesis versus the one-sided alternative that the slope is positive? Explain your answer. P= RN_3878578_8_ {"js_version":0} Conclusion mc We could reject H0 at the 5% significance level. We could not reject H0 at the 5% significance level. 2 The index of biotic integrity (IBI) is a measure of the water quality in streams. IBI and land-use measures for a collection of streams in the Ozark Highland ecoregion of Arkansas were collected as part of a study. The data table below gives the data for IBI, the percent of the watershed that was forest, and the area of the watershed in square kilometers for streams in the original sample with watershed area less than or equal to 70km2. Area Forest IBI Area Forest IBI Area Forest IBI Area Forest IBI 21 0 47 29 0 61 31 0 39 32 0 59 34 0 72 34 0 76 49 3 85 52 3 89 2 7 74 70 8 89 6 9 33 28 10 46 21 10 32 59 11 80 69 14 80 47 17 78 8 17 53 8 18 43 58 21 88 54 22 84 10 25 62 57 31 55 18 32 29 19 33 29 39 33 54 49 33 78 9 39 71 5 41 55 14 43 58 9 43 71 23 47 33 31 49 59 18 49 81 16 52 71 21 52 75 32 59 64 10 63 41 26 68 82 9 75 60 54 79 84 12 79 83 21 80 82 27 86 82 23 89 86 26 90 79 16 95 67 26 95 56 26 100 85 28 100 91 (a) Use numerical and graphical methods to describe the variable IBI. Do the same for area. (Round your answers for x to two decimal places and your answers for s to three decimal places.) IBI: x = IBI: s = area: x = RN_3895485_5_ {"js_version":0} RN_3895485_5_ {"js_version":0} area: s = RN_3895485_5_ {"js_version":0} RN_3895485_5_ {"js_version":0} (b) Plot the data and describe the relationship between IBI and area. mc RC_3895485_5_4 {} Describe the relationship between IBI and area. Are there any outliers or unusual patterns? (c) Give the statistical model for simple linear regression for this problem. mc yi = 1 + 0xi + i, where i ~ N(70, ) yi = 1 + 0xi + i, where i ~ N(0, ) yi = 0 + 1xi + i, where i ~ N(0, ) yi = 0 + 1xi + i, where i ~ N(70, ) yi = 0 + 1xi + i, where i ~ N(35, ) RC_3895485_5_6 {} (d) State the null and alternative hypotheses for examining the relationship between IBI and area. mc H0: 0 = 0; Ha: 0 0 H0: 1 = 0; Ha: 1 < 0 H0: 0 = 0; Ha: 0 > 0 H0: 1 = 0; Ha: 1 0 H0: 1 = 0; Ha: 1 > 0 RC_3895485_5_7 {} (e) Run the simple linear regression and summarize the results. (Let x = area and y = IBI. Round your answers to three decimal places.) y= + xs= RN_3895485_5_ {"js_version":0} RN_3895485_5_ r= {"js_version":0} RN_3895485_5_ {"js_version":0} (f) Obtain the residuals and plot them versus area. mc {"js_version":0} RN_3895485_5_ RC_3895485_5_1 {} Is there anything unusual in the plot? mc The residual plot seems to have a positive linear relationship. about the plot. There is nothing unusual The residual plot shows that there is more variation for large area. residual plot shows that there is more variation for small area. The The residual plot seems to have a negative linear relationship. RC_3895485_5_1 {} (g) Do the residuals appear to be approximately Normal? Give reasons for your answer. mc The residuals are somewhat right-skewed and not close to Normal. somewhat left-skewed but, otherwise close to Normal. skewed and not close to Normal. Normal. The residuals are The residuals are somewhat left- The residuals are completely scattered and not close to The residuals are somewhat right-skewed but, otherwise close to Normal. RC_3895485_5_1 {} (h) Do the assumptions for the analysis of these data using the model you gave in part (c) appear to be reasonable? Explain your