Question

According to the Vivino website, the mean price for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is $32.48. A New England–based lifestyle magazine wants to determine if red wines of the same quality are less expensive in Providence, and it has collected prices for 56 randomly selected red wines of similar quality from wine stores throughout Providence. The mean and standard deviation for this sample are $30.15 and $12, respectively. Develop appropriate hypotheses for a test to determine whether the sample data support the conclusion that the mean price in Providence for a bottle of red wine that scores 4.0 or higher on the Vivino Rating System is less than the population mean of $32.48. Use alpha=0.10

Establish the two hypotheses
Calculate the test statistic
Make a decision using the critical value approach
Make a decision using the p-value approach

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 32.48
Alternative Hypothesis, Ha: μ < 32.48

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (30.15 - 32.48)/(12/sqrt(56))
t = -1.453

Rejection Region
This is left tailed test, for α = 0.1 and df = 55
Critical value of t is -1.297.
Hence reject H0 if t < -1.297

reject the null hypothesis

P-value Approach
P-value = 0.0760
As P-value < 0.1, reject the null hypothesis.