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	239	242	265	245	259	248
225	226	251	233

A vertical boxplot has a vertical axis labeled "Calories" with values from 223 to 267. The top whisker is approximately at 265.0, the top-most edge of the box is near 253.0, the line inside the box is approximately 244.5, the bottom-most edge of the box is near 236.0, and the bottom whisker is at approximately 225.0.

A scatterplot has 12 points. The plot's horizontal axis is labeled "Normal score" and ranges from −1.7 to 1.7. Its vertical axis is labeled "Calories" and ranges from 223 to 267. There is one point plotted near (−1.7, 225) and a second near (−1.1, 227). After the second point, the 10 remaining points are plotted from left to right in upward, mostly diagonal direction. The pattern begins near the bottom left of the diagram and ends at approximately (1.7, 265). The distance between each point varies slightly. All points are between the approximate horizontal axis values of −1.7 and 1.7 and between the approximate vertical axis values of 223 and 267.

(a) Is it reasonable to test hypotheses about true average calorie content μ by using a t test?

o Yes, it is reasonable

o No, t test is not applicable here.   

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?

o Yes, it is clear that true average content differs from the stated value

o No, it is possible that true average content is 243.  

o 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 α = 0.05. Round your test statistic to two decimal places and your P-value to three decimal places.)

t	=
df	=
P	=

Conclusion:

o Reject H₀

o Fail to reject H₀.    

(everything bold needs an answer).

Answer 1

(a) Yes, it is reasonable

(b) No, it is possible that true average content is 243.

(c) Sample mean using excel function AVERAGE(), x̅ = 244.3333

Sample standard deviation using excel function STDEV.S, s = 12.3828

Sample size, n = 12

Test statistic:  

t = (x̅ - µ)/(s/√n) = (244.3333 - 243)/(12.3828/√12) = 0.37

df = n-1 = 11

Two tailed p-value = T.DIST.2T(ABS(0.37), 11) = 0.7162

Conclusion:

Fail to reject H0.