Catalina read a report saying that the average daily high temperature in Buenos Aires a few years ago was $18.2^{\circ} \mathrm{C}$. She believes that last year was warmer than this. To test her belief, she takes a simple random sample of 20 days from last year and records the daily high temperature on each chosen day. Let $\mu$ represent the average daily high temperature in Buenos Aires last year. Which of the following is an appropriate set of hypotheses for Catalina's significance test? Choose 1 answer: (A) $$ \begin{array}{l} H_{0}: \mu=18.2^{\circ} \mathrm{C} \ H_{\mathrm{a}}: \mu18.2^{\circ} \mathrm{C} \ H_{\mathrm{a}}: \mu=18.2^{\circ} \mathrm{C} \end{array} $$ (C) $$ \begin{array}{l} H_{0}: \mu=18.2^{\circ} \mathrm{C} \ H_{\mathrm{a}}: \mu18.2^{\circ} \mathrm{C} \end{array} $$ (D) $$ \begin{array}{l} H_{0}: \mu18.2^{\circ} \mathrm{C} \ H_{\mathrm{a}}: \mu \neq 18.2^{\circ} \mathrm{C} \end{array} $$

Question

Catalina read a report saying that the average daily high temperature in Buenos Aires a few years ago was $18.2^{\circ} \mathrm{C}$. She believes that last year was warmer than this. To test her belief, she takes a simple random sample of 20 days from last year and records the daily high temperature on each chosen day.

Let $\mu$ represent the average daily high temperature in Buenos Aires last year.

Which of the following is an appropriate set of hypotheses for Catalina's significance test?

Choose 1 answer:
(A)
$$
\begin{array}{l}
H_{0}: \mu=18.2^{\circ} \mathrm{C} \
H_{\mathrm{a}}: \mu<18.2^{\circ} \mathrm{C}
\end{array}
$$
(B)
$$
\begin{array}{l}
H_{0}: \mu>18.2^{\circ} \mathrm{C} \
H_{\mathrm{a}}: \mu=18.2^{\circ} \mathrm{C}
\end{array}
$$
(C)
$$
\begin{array}{l}
H_{0}: \mu=18.2^{\circ} \mathrm{C} \
H_{\mathrm{a}}: \mu>18.2^{\circ} \mathrm{C}
\end{array}
$$
(D)
$$
\begin{array}{l}
H_{0}: \mu>18.2^{\circ} \mathrm{C} \
H_{\mathrm{a}}: \mu \neq 18.2^{\circ} \mathrm{C}
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the correct null hypothesis (H₀) based on the scenario. Since Catalina wants to test if the average temperature is higher than the reported average, the null hypothesis should state that the average temperature is equal to the reported average. ‖ ‖ step 2 ⋮ Formulate the alternative hypothesis (Hₐ) based on Catalina's belief. She believes that the average temperature is higher, so the alternative hypothesis should reflect that the average temperature is greater than the reported average. ‖ ‖ step 3 ⋮ Choose the appropriate set of hypotheses. The null hypothesis should be that the average temperature is equal to 18.2°C, and the alternative hypothesis should be that the average temperature is greater than 18.2°C. ‖ ***C*** ∻Key Concept∻ ⚹Hypothesis Testing⚹ ∻Explanation∻ ⚹In hypothesis testing, the null hypothesis (H₀) typically states that there is no effect or no difference, and it is what we assume to be true before collecting data. The alternative hypothesis (Hₐ) is what we want to test for; it is a statement that there is an effect or a difference. In this case, since Catalina believes the temperature is higher, Hₐ should reflect that belief.⚹◊What is the formula for the calculation of the test statistic for Catalina's significance test in hypothesis testing?⍭ Generate me a similar question◊

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