Example 175 below describes the study of sweetness loss in c

Example 17.5 (below) describes the study of sweetness loss in colas. Diet colas use artificial sweeteners to avoid sugar. These sweeteners gradually lose their sweetness over time. Manufacturers therefore test new colas for loss of sweetness before marketing them. Trained tasters sip the cola along with drinks of standard sweetness and score the cola on a sweetness score of 1 to 10, with larger scores corresponding to greater sweetness. The cola is then stored for a month at high temperature to imitate the effect of four months\' storage at room temperature. Each taster scores the cola again after storage. This is a matched pairs experiment. Our data are the differences (score before storage minus score after storage) in the tasters\' scores. The bigger these differences, the bigger the loss of sweetness. Suppose we know that for any cola, the sweetness loss scores vary from taster to taster according to a Normal distribution with standard deviation ? = 1. The mean ? for all tasters measures loss of sweetness and is different for different colas. The study of sweetness loss in Example 17.3 tests the hypotheses H0: ? = 0 Ha: ? > 0 Example 17.5 gives the mean sweetness loss for two colas: For the first cola, the 10 tasters found mean sweetness loss x = 0.3. For the second, the data gave x = 1.02. The Normal curve is the sampling distribution of x when the null hypothesis H0 : ? = 0 is true. The P-value for the first cola in Example 17.5 is the probability (taking the null hypothesis ? = 0 to be true) that x takes a value at least as large as 0.3. Step 1: For the first cola, what is the sampling distribution of x when ? = 0? This distribution appears in Figure 17.2. A. Normal distribution with mean 0.3 and standard deviation 0.3162. B. Normal distribution with mean 0 and standard deviation 0.3162. C. Normal distribution with mean 0 and standard deviation 0.1. D. Normal distribution with mean 0 and standard deviation 1. Step 2: Do a Normal probability calculation to find the P-value, for the first cola. A. 0.3422 B. 0.1711 C. 0.8289 D. 0.1645

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