Question

Math

Posted 5 months ago

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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)
$\begin{array}{l}
H_{0}: p_{\$ 10}-p_{20 \%} \neq 0 \\
H_{\mathrm{a}}: p_{\$ 10}-p_{20 \%}=0
\end{array}$
```

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Answer from Sia

Posted 5 months ago

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.

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