Mauricio Tersignico, a local wine merchant, wants to determine if the average price of domestic wine
is less than the average price of imported wine.The data obtained is shown in the table below.
-What is the test value? Use (Use the variances unequal formula.)
A)-6.97
B)-2.50
C)-4.53
D)-2.54

Question

Mauricio Tersignico, a local wine merchant, wants to determine if the average price of domestic wine
is less than the average price of imported wine.The data obtained is shown in the table below. 
-What is the test value? Use  (Use the variances unequal formula.)
A)-6.97 
B)-2.50 
C)-4.53 
D)-2.54

Quizplus · Accepted Answer

To find the test value, we need to first calculate the pooled standard deviation using the formula: 
s_p = sqrt{((n1-1)s1^2 + (n2-1)s2^2)/(n1+n2-2)} 
s1 and s2 are the sample standard deviations for domestic and imported wines, respectively, n1 and n2 are the sample sizes. 
Substituting the values, we get s_p = sqrt{((20-1)10.62^2 + (25-1)11.82^2)/(20+25-2)} = 11.18 
Then, we can calculate the t-value using the formula: 
t = (x1 - x2) / (s_p * sqrt(1/n1 + 1/n2)) 
Where x1 and x2 are the sample means for domestic and imported wines, respectively. 
Substituting the values, we get t = (30.45 - 36.56) / (11.18 * sqrt(1/20 + 1/25)) = -2.54. 
Since we are using the variances unequal formula, we are assuming that the population variances for domestic and imported wines are not equal. Hence, we use the t-distribution with degrees of freedom given by: 
df = [(s1^2/n1 + s2^2/n2)^2] / [((s1^2/n1)^2/(n1-1) + (s2^2/n2)^2/(n2-1))] 
Substituting the values, we get df = [(10.62^2/20 + 11.82^2/25)^2] / [((10.62^2/20)^2/19 + (11.82^2/25)^2/24)] = 39.56 (rounded to nearest integer). 
Looking up the t-distribution table with 39 degrees of freedom and level of significance 0.05, we find the critical value to be -2.022. 
Since our calculated t-value (-2.54) is less than the critical value (-2.022), we reject the null hypothesis and conclude that the average price of domestic wine is less than the average price of imported wine at a significance level of 0.05.

Mauricio Tersignico, a Local Wine Merchant, Wants to Determine If