# res - 9.52 At Ajax Spring Water a half-li ter bottle of...

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At Ajax Spring Water, a half-liter bottle of soft drink is supposed to contain a mean of 520 ml. The filling process follows a normal distribution with a known process standard deviation of 4 ml. (a) Which sampling distribution would you use if random samples of 10 bottles are to be weighed? Why? Mean of the sample means: 520 ml St. Dev. of the sample means: 4/sqrt(10) Both are prescribed by the Central Limit Theorem (b) Set up hypotheses and a two-tailed decision rule for the correct mean using the 5 percent level of significance. Ho: mean = 520 Ha: mean is not 520 Reject Ho if z(mean of the sample) is > 1.96 or <-1.96 (c) If a sample of 16 bottles shows a mean fill of 515 ml, does this contradict the hypothesis that the true mean is 520 ml? z(515) = (515-520)/[4/sqrt(10)]= -3.9528. .. Yes, it is evidence the mean is not 520. 9.58 Given information isA sample of 100(n) mortgages approved during the current year showed that 31(X) were issued toa single-earner family or individual. The historical averageis 25(P = 0.25) percent. Sample proportion = p =X/n = 31/100 = 0.31

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res - 9.52 At Ajax Spring Water a half-li ter bottle of...

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