Many consumers pay careful attention to stated nutritional contents on packaged

Question

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 desirable!) Here are the resulting observations, along with a boxplot and normal probability plot. (To obtain the dataset for your analysis software, go to the Book Companion Website.) 255 244 243 265 245 259 248 225 226 251 233 (a) Is it reasonable to test hypotheses about true average calorie content mu by using a t test? (b) The stated calorie content is 240. Does the boxplot suggest that true average content differs from the stated value? Yes, it is clear that true average content differs from the stated value. No, it is possible that true average content is 240. C There's not enough evidence to decide. (c) Carry out a formal test of the hypotheses suggested in part (b). (Use Table 4 in Appendix A. Use = 0.05. Round your test statistic to two decimal places and your P-value to three decimal places.)

Explanation / Answer

Answers to the question:

a. Yes, it is reasonable
b. Yes, it is clear that true average content differs from the stated value
c.

alpha = .05
Stdev from sample = 11.86
pop. mean = 240
Sample mean = 244.33

t = (244.33-240)/(11.86/sqrt(6)) = .894

At alpha = .05 , The two-tailed P value equals 0.4142

  

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