d) It\'s illegal to sell beer n Utah that\'s higher than 4% alcohol-by-volume (A
ID: 3362608 • Letter: D
Question
d) It's illegal to sell beer n Utah that's higher than 4% alcohol-by-volume (ABV) Prohibition Brewing wants to see whether a new batch of ale has an ABV higher than the legal lint A sample of 100 bottles has a mean of 52% ABV. The population standard devaten is 4%, and the sgnificance level is 5%. You don't need t decimals whale doing this problem) coavert the percentages to 1) State the null and the altermative hypotheses for the test. 2) Caleulate the value of the test statistic and the p-vahue 3) What is oar formal coachasion Will at be legal to sell the ale in UtahExplanation / Answer
1)
Null Hypothesis H0: The batch of ale has ABV less than or equal to the legal limit of 4%.
Alternative Hypothesis Ha: The batch of ale has ABV is greater than the legal limit of 4%.
2)
As, we know the population standard deviation, we will perform one sample z test.
Standard error of the sampling distribution of mean, SE = SD / sqrt(n) = 4 / sqrt(100) = 0.4
Test statistic, z = (Observed Mean - Hypothesized Mean) / SE = (5.2 - 4) / 0.4 = 3
P-value = P(Z > 3) = 0.00135
3)
As, P-value is less than the significance level of 0.05 (5%), we reject the null hypothesis and conclude that batch of ale has ABV greater than the legal limit of 4%.
So, it will be illegal to sell the ale in Utah.
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