The data in the accompanying table represent the rate of return of a certain company stock for 11​ months, compared with the rate of return of a certain index of 500 stocks. Both are in percent. Complete parts ​(a) through ​(d) below. ​(a) Treating the rate of return of the index as the explanatory​ variable, x, use technology to determine the estimates of β0 and β1.   The estimate of β0 is ____? ​(Round to four decimal places as​ needed.)   The estimate of β1 is ____? ​(Round to four decimal places as​ needed.) (b) Assuming the residuals are normally​ distributed, test whether a linear relation exists between the rate of return of the​ index, x, and the rate of return for the company​ stock, y, at the α=0.10 level of significance. Choose the correct answer below.   State the null and alternative hypotheses.   A. H0​: β0=0 H1​: β0≠0   B. H0​: β0=0 H1​: β0>0   C. H0​: β1=0H1​: β1≠0   D. H0​: β1=0 H1​: β1>0   Determine the​ P-value for this hypothesis test.   ​P-value=_____? ​(Round to three decimal places as​ needed.)   State the appropriate conclusion at the α=0.10 level of significance. Choose the correct answer below.   A. Do not reject H0. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.   B.Reject H0. There is sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.   C. Reject H0. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.     D. Do not reject H0. There is not sufficient evidence to conclude that a linear relation exists between the rate of return of the index and the rate of return of the company stock.    ​(c) Assuming the residuals are normally​ distributed, construct a​ 90% confidence interval for the slope of the true​ least-squares regression line.   Lower​ bound: = ​(Round to four decimal places as​ needed.)   Upper​ bound: = ​(Round to four decimal places as​ needed.)   ​(d) What is the mean rate of return for the company stock if the rate of return of the index is 3.25​%?   The mean rate of return for the company stock if the rate of return of the index is 3.25​% is  ______​%? ​(Round to three decimal places as​ needed.)

It has been determined that there is a significant relationship between the temperature (x) and the number of times that a cricket chirps in a minute (y). Below is a table of values: Number of Temperature chirps 69.7 882 93.3 1188 84.3 1104 76.3 864 88.6 1200 82.6 1032 71.6 960 79.6 900

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. 203 x days y km/100 72 76 32 14.7 94 11.7 19.5 5.3 35.6 (a) Verify that Ex = 477, Ey = 86.8, Ex? = 62,029, Ey2 = 2028.68, Exy = 11036.6, and r= 0.93853. Ex Ey Ex? Ey2| Exy (b) Use a 1% level of significance to test the claim p> 0. (Use 2 decimal places.) critical t Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. Reject the null hypothesis, there is insufficient evidence that p > 0. O Fail to reject the null hypothesis, there is insufficient evidence that p > 0. O…

Ocean currents are important in studies of climate change, as well as ecology studies of dispersal of plankton. Drift bottles are used to study ocean currents in the Pacific near Hawaii, the Solomon Islands, New Guinea, and other islands. Let x represent the number of days to recovery of a drift bottle after release and y represent the distance from point of release to point of recovery in km/100. The following data are representative of one study using drift bottles to study ocean currents. x days y km/100 71 76 31 92 203 14.2 19.6 5.8 11.2 35.9 (a) Verify that Ex = 473, Ey = 86.7, Ex = 61,451, Ey = 2033.69, Exy = 10995.7, and r 0.93868. %3D %3D %3D %3D Σχ 1 473 ΣΥ| 86.7 Ex2 61451 Ey2 2033.69 Exy 10995.7 r0.93868 (b) Use a 1% level of significance to test the claim p > 0. (Use 2 decimal places.) t 4.72 critical t 4.54 Conclusion Reject the null hypothesis, there is sufficient evidence that p > 0. O Reject the null hypothesis, there is insufficient evidence that p > 0. Fail to reject…