I attached the data from #2

I am confused on this, question #5

2. Madison 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 fire hose, dragging a weighted object, and crawling in a simulated attic environment. The times, in seconds, for recruits to complete the test for 30 randomly chosen Madison firefighter are: 403 422 3?5 318 275 332 243 266 298 247 285 332 264 249I 358 356 332 425 351 372 264 348 362 413 325 396 350 379 365 416 Note that Ex, = 10121 and the population standard deviation 56 is given for convenience. Construct a 90% condence interval for the population mean time to complete the test for Madison firefighter. (Round the values to 2 decimal places, e.g., 12.34) (a) Check the three assumptions. (b) Find out the three components for the 90% confidence interval. (c) Calculate and interpret the 90% confidence interval for the population mean time. (Please see page 15 on the Chapter 8 slide and the solved examples for the interpretation.) (d) Suppose we increase the confidence level while the sample size is still fixed. Then, the width of the confidence interval becomes: narrower / wider 5. With reference to question 2 in this HW, test whether the population mean time to complete the test for Madison fire-fighter is greater than 310 seconds under 0.05 significance level. (We omit the first step as the assumptions are checked in question 2.) (a) State the null and alternative hypotheses. (b) Calculate the test statistic z*. (c) Compute the p-value. (d) Draw a conclusion regarding the null hypothesis and interpret the result based on the alternative hypothesis. (Please see page 32 on the Chapter 8 slide and the solved examples for the conclusion and interpretation.)