The manufacturers of soft drink P claim that consumers \' prefer their drink to
ID: 3368231 • Letter: T
Question
The manufacturers of soft drink P claim that consumers ' prefer their drink to that of arch-rival soft drink c. To test this claim, a booth was set up at a state fair and randomly chosen persons asked to give a preference be tween (unmarked) cups of P and C. tOne might criticize this sample -fair-goers may not be typical of soft drink consumers.1 Suppose 145 of 2S0 persons preferred soft drink P; the remainder preferred C. Formulate and perform an appropriata statistical test to test the manufacturers' cilaim. lwhat is the attained significance level what should we conclude?Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: P < 0.50
Alternative hypothesis: P > 0.50
Note that these hypotheses constitute a one-tailed test.
Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.
Analyze sample data. Using sample data, we calculate the standard deviation (S.D) and compute the z-score test statistic (z).
S.D = sqrt[ P * ( 1 - P ) / n ]
S.D = 0.03162
z = (p - P) / S.D
z = 2.53
where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.
Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.53.
Thus, the P-value = 0.006
Interpret results. Since the P-value (0.006) is less than the significance level (0.05), we cannot accept the null hypothesis.
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