High School

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Customers who participate in a store's free loyalty card program save money on their purchases but allow the store to track their shopping habits and potentially sell this data to third parties. A survey revealed that 220 out of a random sample of 250 adults in a certain country would agree to participate in a store loyalty card program, despite the potential for information sharing. Let [tex]p[/tex] represent the true proportion of all customers who would participate in a store loyalty card program.

Consider a store owner who claims that more than 81% of all customers would participate in a loyalty card program. Set up the null and alternative hypotheses for testing whether the true proportion of all customers who would participate in a store loyalty card program exceeds 0.81.

[tex]H_0: p = 0.81[/tex]

[tex]H_a: p > 0.81[/tex]

Answer :

The null hypothesis (H0) for testing the store owner's claim that more than 81% of customers would participate in a loyalty card program is p \\u2264 0.81. The alternative hypothesis (Ha) is p > 0.81.

The student's question involves setting up null and alternative hypotheses for hypothesis testing involving a proportion. The store owner's claim that more than 81% of all customers would participate in a loyalty card program is a statement about a population proportion. In hypothesis testing, the null hypothesis typically includes an equality condition (<=, =, or >=), which in this case would mean that the proportion is equal to or less than 0.81. The alternative hypothesis reflects the research hypothesis that the true proportion is greater than 0.81.

Here are the null and alternative hypotheses for testing whether the true proportion of all customers who would participate in a store loyalty card program exceeds 0.81:

  • Null Hypothesis (H0): p ≤ 0.81
  • Alternative Hypothesis (Ha): p > 0.81

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