Kara works for a website that is considering sending emails with different types of coupons to its customers. She suspects that coupons offering $\$ 10$ off will be used more often than coupons offering $20 \%$ off. She plans on sending each type of coupon to a separate random sample of users. She'll then test if the proportion of customers who use the $\$ 10$ off coupon is significantly larger than the proportion who use the $20 \%$ off coupon. Which of the following is an appropriate set of hypotheses for Kara's significance test? Choose 1 answer: (A) $$ \begin{array}{l} H_{0}: p_{\$ 10}-p_{20 \%}=0 \ H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}0 \end{array} $$ (C) $$ \begin{array}{l} H_{0}: p_{\$ 10}-p_{20 \%}=0 \ H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%} \neq 0 \end{array} $$ (D) $$ \begin{array}{l} H_{0}: p_{\$ 10}-p_{20 \%} \neq 0 \ H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}=0 \end{array} $$

Question

Kara works for a website that is considering sending emails with different types of coupons to its customers. She suspects that coupons offering $\$ 10$ off will be used more often than coupons offering $20 \%$ off. She plans on sending each type of coupon to a separate random sample of users. She'll then test if the proportion of customers who use the $\$ 10$ off coupon is significantly larger than the proportion who use the $20 \%$ off coupon.

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

Choose 1 answer:
(A)
$$
\begin{array}{l}
H_{0}: p_{\$ 10}-p_{20 \%}=0 \
H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}<0
\end{array}
$$
(B)
$$
\begin{array}{l}
H_{0}: p_{\$ 10}-p_{20 \%}=0 \
H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}>0
\end{array}
$$
(C)
$$
\begin{array}{l}
H_{0}: p_{\$ 10}-p_{20 \%}=0 \
H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%} \neq 0
\end{array}
$$
(D)
$$
\begin{array}{l}
H_{0}: p_{\$ 10}-p_{20 \%} \neq 0 \
H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}=0
\end{array}
$$

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Identify the claim Kara is testing. ‖ ‖ step 2 ⋮ Formulate the null hypothesis ($H_0$) and alternative hypothesis ($H_a$) based on the claim. ‖ ‖ step 3 ⋮ Since Kara suspects that the $10 off coupon will be used more often, the alternative hypothesis should reflect that the proportion for the $10 off coupon is greater than the 20% off coupon. ‖ ‖ step 4 ⋮ The correct null hypothesis should state there is no difference in proportions, and the alternative hypothesis should reflect Kara's claim. ‖ ∻[question number] Answer∻ ⚹ (B) $H_0: p_{\$10} - p_{20\%} = 0$, $H_a: p_{\$10} - p_{20\%} > 0$ ⚹ ∻Key Concept∻ ⚹Hypothesis Testing⚹ ∻Explanation∻ ⚹In hypothesis testing, the null hypothesis ($H_0$) typically states that there is no effect or no difference, and the alternative hypothesis ($H_a$) states the researcher's belief or the claim to be tested. Since Kara believes the $10 off coupon will be used more often, the alternative hypothesis should indicate that the proportion of customers using the $10 off coupon is greater than the proportion using the 20% off coupon.⚹◊What is the importance of choosing the correct null and alternative hypotheses in a significance test related to proportions?⍭ Generate me a similar question◊

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