Please answer in 20 minututes

weekly sales 225.5501 262.7071 250.8194 279.433 285.5992 377.1537 341.7679 265.6971 314.1253 318.3874 238.9874 267.2385 210.7583 299.8066 316.8308 336.6987 326.1876 319.643 411.65 220.3247 272.2544 323.1615 254.4559 244.8675 168.1432 197.3255 351.7762 351.7001 258.7254 372.6192 303.7682 301.9962 299.2844 271.1578 294.3758 324.8062

Use the information above to answer the questions below. (8 points) Our company produces personal computers and is considering the introduc- tion of new color options for the hardware in the hope of boosting sales. Maintaining production of more than one color of computer is costly. So it is important to measure whether introducing new colors is profitable. In doing so, the company focuses on how many units of the new color are sold per week (weekly sales). The marketing department introduced and advertised the new colors in a test mar- keting experiment over 36 weeks (which is the sample). The weekly sales during the experiment are given in the Excel file. Before launching the new products, the mar- keting department estimated that, on average, 280 units of the new color are sold per week.

(a) (2 points) To test the validity of the estimation made by the marketing depart- ment, What is (the value of) the test statistics?

(b) (2 points) Can you reject the claim with 95% confidence? (c) (2 points) What is (the value of) the p-value? (d) (2 points) Suppose you can reject the claim with a confidence level of x. What is the range of x?