Pension Plan 1: A firm is interested in studying the relationship between participation in a 401k pension plan and the generosity of the plan. A random sample of n = 50 pension plans for similar firms in the same industry was collected. Data included the participation rate as a percent (prate), the 401k plan match rate (mrate)*, the total number of 401k participants (totpart), the total number of eligible employees for the 401k plan (totelg), the age of the 401k plan (age), and the total number of employees at the firm (totemp). * The 401k match rate (mrate) measures the generosity of the plan and gives the average amount the firm contributes to each worker's plan for each $1 contribution by the worker. For example, if mrate = $0.50, then a $1 contribution by the worker is matched by a 50c contribution by the firm. Build a regression model to predict participation rate from the other variables listed above. The data are contained in the worksheet named "401K" (Hint: There are more variables in the worksheet than you are instructed to use here: Be sure to construct the correct models specified in these instructions). (a) State the model equation. O PRATE = 1MRATE + $2TOTPART + B3TOTELG + B4AGE + $5TOTEMP O MRATE = 1PRATE + 2TOTPART + 83TOTELG + B4AGE + 35TOTEMP O TOTEMP = Bo + 1PRATE + 2TOTPART + B3TOTELG + B4AGE + BSPRATE O PRATE = Bo + 1MRATE + 2TOTPART + 83TOTELG + B4AGE + B5TOTEMP O MRATE = Bo + 1PRATE + 2TOTPART + B3TOTELG + 4AGE + B5TOTEMP (b) Provide the sample-based model coefficient for match rate. (Round your answer to three decimal places.) % Interpret the model coefficient for match rate (MRATE) by mentally inserting the ABSOLUTE VALUE of the coefficient in the blanks below. O According to the sample data, participation rate increases on average by % for every additional dollar in match rate. O According to the sample data, participation rate decreases on average by % for every additional dollar in match rate. O According to the sample data, match rate increases on average by $_ for every additional percentage point in participation rate. O According to the sample data, match rate decreases on average by $_ for every additional percentage point in participation rate. (c) Test the significance of match rate in determining participation rate after accounting for the effects of all the other explanatory variables. Use a 10% significance level. State the hypotheses to be tested. O Ho: B2 = 0 Ha: B2 # 0 O Ho: B1 = 0 Ha: B1 # 0 O Ho: B3 = 0 Ha: B3 # 0(c) Test the significance of match rate in determining participation rate after accounting for the effects of all the other explanatory variables. Use a 10% significance level. State the hypotheses to be tested. O Ho: B2 = 0 Ha : B2 # 0 O Ho: B1 = 0 Ha: B1 $ 0 O Ho: B3 = 0 Ha: 3 # 0 O Ho: B4 = 0 Ha: B4 # 0 O Ho: Bo = 0 Ha: Bo # 0 Interpret the hypotheses you specified above. O Ho: All of the explanatory variables are important in explaining/predicting participation rate. Ha: None of the explanatory variables are important in explaining/predicting participation rate. O Ho: None of the explanatory variables are important in explaining/predicting participation rate. Ha: At least one explanatory variable is important in explaining/predicting participation rate. O Ho: There is no linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ha: There is a linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. O Ho: There is a linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ha: There is no linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. State the decision rule. O Reject Ho if p value 0.10. O Reject Ho if p value > 0.05. Do not reject Ho if p value s 0.05. O Reject Ho if p value > 0.10. Do not reject Ho if p value s 0.10.State the appropriate test statistic name, degrees of freedom, test statistic value, and the associated p-value (Enter your degrees of freedom as a whole number, the test statistic value to three decimal places, and the p-value to four decimal places). ---Select--- ] ( 7) = 0 J,p -Select-- State your conclusion. O Reject the null hypothesis: Yes, participation rate and match rate appear to be linearly related even after accounting for the effects of the other explanatory variables. O Reject the null hypothesis: No, participation rate and match rate do NOT appear to be linearly related even after accounting for the effects of the other explanatory variables. O Do not reject the null hypothesis: Yes, participation rate and match rate appear to be linearly related even after accounting for the effects of the other explanatory variables. O Do not reject the null hypothesis: No, participation rate and match rate do NOT appear to be linearly related even after accounting for the effects of the other explanatory variables. (d) Calculate a 90% confidence interval for match rate. (Round your answer to three decimal places). Choose the best interpretation of the confidence interval for match rate you calculated above by mentally inserting those values in the blanks below. O Based on a historical sample of n = 50 pension plans, we are 0.10 confident that the true average increase in participation rate for a 1 dollar increase in match rate for all pension plans (of similar firms) may be as low as $ _ (Lower Bound) or as high as $. (Upper Bound). O Based on a historical sample of n = 50 pension plans, we are 90% confident that the true average increase in participation rate for a 1 dollar increase in match rate for all pension plans (of similar firms) may be as low as (Lower Bound) or as high as $_ (Upper Bound). O Based on a historical sample of n = 50 pension plans, we are 90% confident that the true average increase in match rate for a 1 dollar increase in participation rate for all pension plans (of similar firms) may be as low as $_ (Lower Bound) or as high as $_ (Upper Bound). O Based on a historical sample of n = 50 pension plans, we are 0.10 confident that the true average increase in match rate for a 1 dollar increase in participation rate for all pension plans (of similar firms) may be as low as $ _ (Lower Bound) or as high as $_ (Upper Bound). Choose the best summary of your analysis. O Even though the sample coefficient for match rate (see part b) is definitely NOT 0, the hypothesis test demonstrated that the population coefficient may be 0. However, the confidence interval results do NOT support the hypothesis test results by showing that the true population coefficient may be as low as $_ (Lower Bound) or as high as $_ (Upper Bound). Because 0 falls outside the interval, 0 is NOT a plausible value for the true population coefficient, indicating the match rate is an important variable in explaining participation rate after accounting for all of the other explanatory variables in the model. O Even though the sample coefficient for match rate (see part b) is definitely NOT 0, the hypothesis test demonstrated that the population coefficient may be 0. Furthermore, the confidence interval results support the hypothesis test results by showing that the true population coefficient may be as low as $_ (Lower Bound) or as high as $_ (Upper Bound). Because 0 falls inside the interval, 0 is a plausible value for the true population coefficient, indicating the match rate is NOT an important variable in explaining participation rate after accounting for all of the other explanatory variables in the model. O The sample coefficient for match rate (see part b) is definitely NOT 0 and the hypothesis test demonstrated that the population coefficient definitely is NOT 0. Furthermore, the confidence interval results support the hypothesis test results by showing that the true population coefficient may be as low as $_ - (Lower Bound) or as high as $_ - (Upper Bound). Because 0 falls inside the interval, 0 is a plausible value for the true population coefficient, indicating the match rate is NOT an important variable in explaining participation rate after accounting for all of the other explanatory variables in the model. O The sample coefficient for match rate (see part b) is definitely NOT 0 and the hypothesis test demonstrated that the population coefficient definitely is NOT 0. However, the confidence interval results do NOT support the hypothesis test results by showing that the true population coefficient may be as low as $_ (Lower Bound) or as high as $_ (Upper Bound). Because 0 falls outside the interval, 0 is NOT a plausible value for the true population coefficient, indicating the match rate is an important variable in explaining participation rate after accounting for all of the other explanatory variables in the model