Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtair data shown in the table below.
$\begin{array}{cc}
\hline \text { Imported Wine } & \text { Domestic Wine } \
\hline \bar{X}_{1}=\$ 7.03 & \bar{X}_{2}=\$ 9.78 \
s_{1}=\$ 2.31 & s_{2}=\$ 3.62 \
n=15 & n=16 \
\hline
\end{array}$

What is the appropriate test value for a $t$ test?

Question

Mauricio Cruz, a wine merchant for Cruz's Spirits Emporium, wants to determine if the average price of imported wine is less than the average price of domestic wine. He obtair data shown in the table below.
$\begin{array}{cc}
\hline \text { Imported Wine } & \text { Domestic Wine } \
\hline \bar{X}_{1}=\$ 7.03 & \bar{X}_{2}=\$ 9.78 \
s_{1}=\$ 2.31 & s_{2}=\$ 3.62 \
n=15 & n=16 \
\hline
\end{array}$

What is the appropriate test value for a $t$ test?

Quizplus · Accepted Answer

The appropriate test value for a $t$ test can be calculated using the formula for the difference between two means:$$ t = \frac{\bar{X}_1 - \bar{X}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} $$Plugging in the given values:$$ t = \frac{7.03 - 9.78}{\sqrt{\frac{2.31^2}{15} + \frac{3.62^2}{16}}} $$$$ t \approx -2.54 $$Therefore, the correct test value is -2.54.

Mauricio Cruz, a Wine Merchant for Cruz's Spirits Emporium, Wants