Part. 1 [4 marks] A manufacturer of aluminum alloy rods claims that their product has a mean tensile strength of 275 MPa. We examine a smnple of i} of the rods and reocrd the following tensile stengths (in hips]: 286 272 252 255 269 254 275 274 279 [a] Store the aluminum rod data in an appropriately named vector. Test the research hy- pothesis that the population mean tensile strength of the rods is less than the claimed 275 MPa. Copy and paste the appropriate R command and output. (b) Clearly state the pvalue you found from part (a). What is the strength of the evidence against Hg? it) Write a sentence stating your Conclusion of the hypothesis test you just performed. That is, write your conclusion in plain language so that a non-statistician could understand the conclusion of the test. (:1) Calculate a 99% condence interval (Le. a two-sided condence interval) for the true mean tensile strength of the aluminum alloy rods. Copy and paste the appropriate R command and output. In an additional line, clearly state the 1values you get for the condence interval from your output