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 randomsample 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 destroyingthe product, so a census would certainly not be desirable!) Here are the resulting observations, along with a boxplot and normal probability plot. (Use this dataset for your analysis software.)255 244225270260-250240230220239 242 265 245 259 248226 251 233Calories265255245235225-1.50.5Normal score-0.51.5(a) Is it reasonable to test hypotheses about mean calorie content u by using a t test? Explain why or why not.Ⓒ 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 isappropriate.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.It depends on the results of t test.(b) The stated calorie content is 241. 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 statedvalue.● Not necessarily, it is possible that true average content is 241 and observed differences could be due to sampling variability.O No, the true average content must be 241 since 241 is inside the box of the boxplot.O Yes, the true average content must be different from 241 since 241 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 two decimal places and your P-value to four decimal places.)t =P-value =State the conclusion in the context of the problem.O Fail to reject Ho. We have convincing evidence that the stated calorie content is not 241.O Reject H₂. We do not have convincing evidence that the stated calorie content is not 241.● Fail to reject Ho. We do not have convincing evidence that the stated calorie content is not 241.O Reject Ho. We have convincing evidence that the stated calorie content is not 241.

Question

Accepted Answer

The data shows the calorie content of 12 frozen dinners.

(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 two decimal places and your P-value to four decimal places.) P-value =