Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases. It is therefore important that the information on packages be accurate. A random sample of n 12 frozen dinners of a certain type was selected from production during a particular period, and the calorie content of each one was determined. (This determination entails destroying the product, so a census would certainly not be desirablet) Here are the resulting observations, along with a boxplot and normal probability plot. (Use this dataset for your analysis software.) 255 244 239| 242 265 245 259 248 225 226 251 233 A USE SALT 27아 265 260 255 - 250- 245- 240 235 23아 225 -1.5 -0.5 0.5 1.5 22아 Normal score (a) Is it reasonable to test hypotheses about mean calorie content u by using a t test? Explain why or why not. O Yes, it is reasonable. The pattern in the normal probability plot is roughly linear, and since the sample was a random sample from the population, the t test is appropriate. O No, the t test is not applicable here. The pattern in the normal probability plot is roughly linear. Therefore, the t test is not appropriate. O Yes, it is reasonable. The pattern in the normal probability plot is not linear, and since the sample was a random sample from the population, the t test is appropriate. O No, the t test is not applicable here. The sample was not a random sample from the population so the t test is not appropriate. O It depends on the results of t test. (b) The stated calorie content is 243. Does the boxplot suggest that true average content differs from the stated value? Explain your reasoning. O Yes, the center of the boxplot is different from the stated value indicating the true average content must differ from the stated value. O Not necessarily, it is possible that true average content is 243 and observed differences could be due to sampling variability. No, the true average content must be 243 since 243 is inside the box of the boxplot. O Yes, the true average content must be different from 243 since 243 is inside the box of the boxplot. (c) Carry out a formal test of the hypotheses suggested in part (b). Find the test statistic and P-value. (Use a = 0.05. Round your test statistic to one decimal place and your P-value to three decimal places.) P-value - State the conclusion in the context of the problem. O Fail to reject Hg. We do not have convincing evidence that the stated calorie content is not 243. O Reject Hg. We do not have convincing evidence that the stated calorie content is not 243. O Fail to reject Hg. We have convincing evidence that the stated calorie content is not 243. O Reject Hg. We have convincing evidence that the stated calorie content is not 243. Calories