From a practice stats exam with no solutions. Any help appreciated !

8A6 (18 points) A developer of solar panels is investigating the nature of the relationship between the solar cell temperature rise above ambient (Y) and the amount of insulation (megawatts per square centimetres). They test 25 solar cells under a very specific set of conditions. The following output from the statistical package \\texttt{R} illustrate the results: Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) 0.13215 1.51447 0.087 0.931 Insulation 0.36200 0.03211 11.275 7.59e-11 (a) [2 marks] Based on the R output, write down the fitted regression model. (b) [2 marks] What is the predicted value of temperature rise for an insulation value of 44? (c) [4 marks] Consider the test in the output that has resulted in a p-value of 7.59e1 1. Write down the corresponding hypotheses for the test and draw a conclusion based on this test. (d) [4 marks]What is the 95% confidence interval for the slope? Interpret the confidence interval in the context of the question. (e) [6 marks] Suppose that before this experiment began, the researchers had felt that the slope of the true regression line would be 0.30. Conduct a statistical test to verify the researchers' claim