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Question 686:



No answer provided yet.We will want to use a 1-sample z-test against the criteria since we are given the population standard deviation.

First we need to formulate the hypotheses:
  1. The Null hypothesis is that the average grams of fat in the orange juice is less than or equal to 2 grams: Ho: μ 2
  2. The alternative hypothesis is the amount of fat is greater than 2 grams : Ha: μ > 2
The test statistic is z*. We will use the following steps to build the z*.
  1. Find the difference between the sample mean and test mean = 2.5-2 = .5
  2. Calculate the standard error of the mean (SE), which is the standard deviation divided by the square root of the sample size = 1.5/SQRT(35) = .2535
  3. Divide the difference from step 1 by the SE in step 2 = .5/.2535 = 1.972
  4. Lookup the value of z*(1.972) in a normal table or the z-score to percentile calculator to find the 1-sided probability = .0243.
Since .0243 is less than the alpha of .05 we would reject the Null Hypothesis and conclude there IS sufficient evidence to conclude the orange juice contains more than 2 grams of fat.

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