Detroit recruits for the fire department need to complete a timed test that simulates working conditions. It includes placing a ladder against a building, pulling out a section of the fired hose, dragging a weighted object, and crawling in a simulated attic environment. The time in seconds is recorded for each recruit. Test at a significance level of 0.05 that the mean time in seconds to complete this timed test is 290 seconds. Below is the data summary of 29 randomly selected recruits. (Round to the nearest hundredth 0.00) Statistics Variable N Mean SE Mean StDev CoefVar Minimum Maximum Seconds 29 312.48 7.75 41.75 13.36 254.00 417.00 a) What is the null and alternative hypothesis? Ho: Ha: b) What is the test statistic and calculate its value? c) Find the p-value or critical value depending on the test statistic used above. d) What is your decision and interpretation?Find the 95% confidence interval for the true population mean time in seconds to complete the task. Is this confidence interval consistent with the decision above? Explain why or why not