Question

Many consumers pay careful attention to stated nutritional contents on packaged foods when making purchases, so it is important that the information on packages be accurate. Suppose that a random sample of n = 12 frozen dinners of a certain type was selected and the calorie content of each one was determined. Below are the resulting observations, along with a boxplot and normal probability plot.

255 244 239 242 265 245 259 248 225 226 251 233
The box-and-whisker plot has a horizontal axis numbered from 220 to 270. The box-and-whisker is also horizontal. The boxplot labeled "Calories" occurs next. The left whisker is approximately 225, the left edge of the box is approximately 236, the line inside the box is approximately 244.5, the right edge of the box is approximately 253, and the right whisker is approximately 265.

A normal probability plot has 12 points plotted on it. The horizontal axis ranges from −1.5 to 1.5 and is labeled "Normal score." The vertical axis ranges from 225 to 265 and is labeled "Calories." The first point is plotted in the bottom left. The second through twelfth points are plotted from the bottom left towards the top right in roughly the shape of a slanted line. The approximate locations of the points from left to right are as follows:
(−1.6, 225), (−1.1, 226), (−0.8, 233), (−0.5, 239), (−0.3, 242), (−0.1, 244), (0.1, 245), (0.4, 248), (0.6, 251), (0.8, 255), (1.1, 259), (1.7, 265).
Find the test statistic and P-value. (Round your test statistic to one decimal place and your P-value to three decimal places.)
t =
P-value =

Answer 1

The question involves using a Student's t-distribution to analyze the calorie content data of frozen dinners. Due to incomplete information, exact calculations of the t-score and P-value are not provided, but would typically be performed using a T-Test in statistical software or on a calculator.

Step-by-step explanation:

The question involves statistical analysis and interpretation of data gathered from calorie content of frozen dinners and the use of a normal probability plot for hypothesis testing regarding the accuracy of the nutritional information reported. Due to the sample size of n = 12, a Student's t-distribution is utilized instead of a normal distribution for the analysis of the sample data. To find the test statistic and P-value, one can use a statistical calculator or software.

For the given data, calculations would involve first computing the sample mean and standard deviation. Then, the t-score and corresponding P-value can be derived by formulating the null hypothesis that the mean calorie content declared on the packages is as stated, with the given observations opposing or supporting this.

Since instructions to find the t-score are not inherently part of the question, and the P-value calculation is tied to the accuracy of the provided data, which is incomplete, the exact answer cannot be provided. However, to perform the calculations one would normally use functionality such as T-Test with the provided data points (using statistical software or a calculator) to determine if the calorie content differs significantly from what's declared by the manufacturer.