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Red Orchards sells apples. They claim that their apples are "the sweetest in the world" with a sugar content of 20% by mass. Granny Smith's Farmers Co'op believes the sugar content of the apples to be lower than 20%. Hence, they buy 30 apples from Red Orchards and test the sugar content with a machine. They find that the sample has a mean sugar content of 18% by mass and a standard deviation of 2% by mass. They then conduct a significance test with significance level 5%.
State the null and alternative hypothesis of the test.
Explain what a type I error would mean given the context of the test.
Find the probability of making a type I error.
Find the p-value of the test.
Hence state the conclusion of the test.
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