Based on an SRS of 48 winemakers in the same region of Italy

Based on an SRS of 48 winemakers in the same region of Italy, the mean percent of alcohol in their wines is 13.15% with a standard deviation of 0.53. Assuming the sample is large enough for the Central Limit Theorem.

Perform a hypothesis test to determine whether the mean alcohol content is larger than 13%. Using = 0.05 and be sure to state your hypotheses, the name of the correct test. Also, calculate the value of the test statistic, find the P-value, and make a conclusion.

Solution

Hypothesised mean: mu = 13

Sample mean: x_bar = 13.15

Sample size: n = 48

sample standard deviation: s = 0.53

significance level: alpha = 0.05

Null hypotheses: H₀: mu <= 13

Alternative hypotheses: H₁: mu > 13

Here appropriate test would be z test (large samples)

Test statistic:

z = (x_bar - mu)/(s/sqrt(n)) Plugging in values we get

z = (13.15 - 13)/(0.53/sqrt(48)) = 1.961

p-value at z = 1.961 is 0.02494

p-value < alpha   (i.e. 0.02494 < 0.05)

Hence we fail to accept null hypotheses.

i.e. there are sufficient evidences to reject null hypotheses.

Hence we conclude that \"mean alcohol content is larger than 13%\"