Problem

According to the Crown ATM Network, the mean ATM withdrawal is $\$ 67$. PayEAse, Inc. manufacturers an ATM that allows one to pay bills, as well as withdraw money. A review of 40 withdrawals shows the mean withdrawal is $\$ 73$ from a PayEAse ATM machine. Do people withdraw more money from a PayEAse ATM machine?

Determine the appropriate null and alternative hypothesis to answer the question.
\[
\begin{array}{l}
H_{0}: \mu=73 \\
H_{a}: \mu> 67
\end{array}
\]
\[
\begin{array}{l}
H_{0}: \mu=73 \\
H_{a}: \mu> 73
\end{array}
\]
\[
\begin{array}{l}
H_{0}: \mu> 67 \\
H_{a}: \mu=67
\end{array}
\]
\[
\begin{array}{l}
H_{0}: \mu=67 \\
H_{a}: \mu> 67
\end{array}
\]

Answer

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Answer

Final Answer: \(\boxed{H_{0}: \mu=67, H_{a}: \mu>67}\)

Steps

Step 1 :According to the Crown ATM Network, the mean ATM withdrawal is $67. PayEAse, Inc. manufacturers an ATM that allows one to pay bills, as well as withdraw money. A review of 40 withdrawals shows the mean withdrawal is $73 from a PayEAse ATM machine. The question is whether people withdraw more money from a PayEAse ATM machine.

Step 2 :To answer this question, we need to set up a null hypothesis (H0) and an alternative hypothesis (Ha).

Step 3 :The null hypothesis (H0) is usually a statement of no effect or no difference. It's the hypothesis that we assume to be true unless we have significant evidence to prove otherwise. In this case, the null hypothesis would be that the mean withdrawal from a PayEAse ATM machine is equal to the mean withdrawal from the Crown ATM Network, which is $67.

Step 4 :The alternative hypothesis (Ha) is what we would believe if the null hypothesis is proven to be false. In this case, the alternative hypothesis would be that the mean withdrawal from a PayEAse ATM machine is greater than the mean withdrawal from the Crown ATM Network.

Step 5 :So, the appropriate null and alternative hypothesis to answer the question would be: H0: μ=67, Ha: μ>67

Step 6 :Final Answer: \(\boxed{H_{0}: \mu=67, H_{a}: \mu>67}\)

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