Please help me with all parts. Thank you!

Q 1.

The following table gives the gold medal times for every other Summer Olympics for the women's 100 meter freestyle (swimming). Year Time (seconds) 1912 82.2 1924 72.4 1932 66.8 1952 66.8 1960 61.2 1968 60.0 1976 55.65 1984 55.92 1992 54.64 2000 53.8 2008 53.1 Part (a) Decide which variable should be the independent variable and which should be the dependent variable. O Independent: time; Dependent: year O Independent: year; Dependent: timePart (b) Make a scatter plot of the data. Time (seconds) Time (seconds) 90 90 85 85 . 80 80 75 75 70 70 65 65 60 60 55 55 Year Year O 1930 1950 1970 1990 2010 O 1930 1950 1970 1990 2010 Time (seconds) Time (seconds) 90 90 85 85 80 80 75 75 70 70 - 65 65 60 60 55 55 Year Year O 1930 1950 1970 1990 2010 O 1930 1950 1970 1990 2010Part (c) Does it appear from inspection that there is a relationship between the variables? Why or why not? Yes, it appears that the time decreases as the year increases. O No, there is no visible relationship between the variables. Part (d) Calculate the least squares line. Put the equation in the form of: y = a + bx. (Round your answers to three decimal places.) y = - Part (e) Find the correlation coefficient r. (Round your answer to four decimal places.) r= Is the decrease in times significant? Yes O No Part (f) Find the estimated gold medal time for 1932. (Use your equation from part (d). Round your answer to two decimal places.) sec Find the estimated gold medal time for 1984. (Use your equation from part (d). Round your answer to two decimal places.) secEl Part (9) Why are the answers from part (f) different from the chart values? 0 The answers are different because of errors in recording the swimming times. 0 The answers are different because swimmers were slower years ago. 0 The answers are different because the chart values are based on observations and the estimated values are based on the least squares line. 0 The answers will be different each time you calculate a least squares line. El Part (h) Does it appear that a line is the best way to t the data? Why or why not? Q A line is the best way to t the data because the slope of the line is negative and the linear correlation is negative. 0 A line does appear to be the best way to t the data because the data points follow a negative linear trend. 0 A line is the best way to t the data because there is only one correct line that will t a data set. 0 A line is not the best way to t the data because it does not touch all the data points. Use the least squares line to estimate the gold medal time for the 2012 Summer Olympics. (Use your equation from part (d). Round your answer to two decimal places.) Do you think that your answer is reasonable? Why or why not? 0 Yes, because the estimate is positive. 0 No, because 2012 is outside the domain of the least squares line. Additional Materials El eBook A graphing calculator is recommended. Three students, Linda, Tuan, and Javier, are given five laboratory rats each for a nutritional experiment. Each rat's weight is recorded in grams. Linda feeds her rats Formula A, Tuan feeds his rats Formula B, and Javier feeds his rats Formula C. At the end of a specified time period, each rat is weighed again, and the net gain in grams is recorded. Using a signicance level of 10%, test the hypothesis that the three formulas produce the same mean weight gain. (Let 1 = Linda's rats, 2 = Tuan's rats and 3 = Javier's rats.) Weights of Student Lab Rats Linda's rats Tuan's rats Javier's rats 52.4 42.7 39.2 46.1 50.0 El Part (a) State the null hypothesis. 0 H0: At least two of the group means m, [42, [43 are not equal. 0 H01M1=l42=I43 El Part (b) State the alternative hypothesis. 0 Ha: At least two of the group means [41, [42, [43 are not equal. 0 Ha=M1=u2=Ma E] Part (c) Enter an exact number as an integer, fraction, or decimal. we: Enter an exact number as an integer, fraction, or decimal. %; 5 |H State the distribution to use for the test. 0 J" 2 O L" A N 000 'n'n'n 5.75? MN; What is the test statistic? (Round your answer to two decimal places.) |H What is the p-value? (Round your answer to four decimal places.) : Explain what the p-value means for this problem. 0 If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. 0 If H0 is false, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. 0 If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or less than the calculated value. 0 If H0 is true, then there is a chance equal to the p-value that the value of the test statistic will be equal to or greater than the calculated value. Sketch a picture of this situation. Label and scale the horizontal axis, and shade the region(s) corresponding to the p-value. pvalue 1/2(pvalue) o F o 1' 1/2(pvalue) Hapvalue) o F o F El Part (i) Indicate the correct decision ("reject" or "do not reject" the null hypothesis), the reason for it, and write appropriate conclusions. (i) Alpha (Enter an exact number as an integer, fraction, or decimal.) a = (ii) Decision: 0 reject the null hypothesis 0 do not reject the null hypothesis (iii) Reason for decision: 0 Since a > p-value, we reject the null hypothesis. 0 Since a p-value, we do not reject the null hypothesis. 0 Since a