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Two surfers and statistics students collected data on the number of days on which surfers surfed in the last month for 30 longboard (L) users and 30 shortboard ( $S$ ) users. Treat these data as though they were from two independent random samples. Test the hypothesis that the mean days surfed for all longboarders is larger than the mean days surfed for all shortboarders (because longboards can go out in many different surfing conditions). Use a level of significance of 0.05 .
Longboard: $4,9,8,4,7,8,9,6,6,11,12,13,11,13,11,16,14,10,10,19,18,14,11,16,20,20,7,22,19,21$ 문
Shortboard: $6,4,4,6,8,8,6,8,4,7,8,5,9,7,4,15,11,9,11,12,10,15,9,11,12,14,9,21,22,12$
Determine the hypotheses for this test. Choose the correct answer below.
A.
\[
\begin{array}{l}
H_{0}: \mu_{L}=\mu_{S} \\
H_{a}: \mu_{L}< \mu_{S}
\end{array}
\]
D.
\[
\begin{array}{l}
H_{0}: \mu_{L}=\mu_{S} \\
H_{a}: \mu_{L}> \mu_{S}
\end{array}
\]
B.
\[
\begin{array}{l}
H_{0}: \mu_{L} \neq \mu_{S} \\
H_{a}: \mu_{L}=\mu_{S}
\end{array}
\]
E.
\[
\begin{array}{l}
H_{0}: \mu_{L}< \mu_{S} \\
H_{a}: \mu_{L}=\mu_{s}
\end{array}
\]
C.
\[
\begin{array}{l}
H_{0}: \mu_{L}> \mu_{S} \\
H_{a}: \mu_{L}=\mu_{S}
\end{array}
\]
F.
\[
\begin{array}{l}
H_{0}: \mu_{L}=\mu_{S} \\
H_{a}: \mu_{L} \neq \mu_{S}
\end{array}
\]
Answer
The correct hypotheses for this test are: \n \[ \n \begin{array}{l} \n H_{0}: \mu_{L}=\mu_{S} \ \n H_{a}: \mu_{L}>\mu_{S} \n \end{array} \n \]
Step 1 ：The question is asking to determine the hypotheses for a statistical test. The null hypothesis (H0) is usually a statement of no effect or no difference. The alternative hypothesis (Ha) is what you might believe to be true or hope to prove true.
Step 2 ：In this case, we are testing the hypothesis that the mean days surfed for all longboarders is larger than the mean days surfed for all shortboarders. So, the null hypothesis should be that the means are equal, and the alternative hypothesis should be that the mean for longboarders is greater than the mean for shortboarders.
Step 3 ：The correct hypotheses for this test are: \n \[ \n \begin{array}{l} \n H_{0}: \mu_{L}=\mu_{S} \ \n H_{a}: \mu_{L}>\mu_{S} \n \end{array} \n \]
