Questions
BUSI_V 291 202 2024W2 Sample Final Exam (Canvas)
Numerical
Use the following information for Questions 7-9. Pet First offers a free pet birthday gift to members who come to the store on their pet's birthday. James is the membership director and he suspects that the proportion who come to get the free birthday gift is higher for younger (human) members. He collects a random sample from from a group of members ages 40+ years (older) and a group aged 20-39 years (younger), then compares data from the two age groups. He tests the following hypotheses using : H0: HA: He finds the following information, which is also available in the Excel sheet for this question. Proportion who get free birthday gift Sample size Older (40+ years) 0.14 150 Younger (20-39 years) 0.27 100 What is the test statistic for this hypothesis test? Answer to three decimal places. Show your calculations in your Excel file on the sheet for this question so that the instructor can award partial marks.
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Step-by-Step Analysis
To compare the proportions between two age groups, we typically use a two-proportion z-test. Here are the steps and reasoning for all parts of the calculation.
First, restate the given data clearly: Older group (n1 = 150) has proportion p1 = 0.14 of members who get the free birthday gift, so the count is x1 = 0.14 × 150 = 21. Younger group (n2 = 100) has p2 = 0.27......Login to view full explanationLog in for full answers
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Use the following information for Questions 7-9. Pet First offers a free pet birthday gift to members who come to the store on their pet's birthday. James is the membership director and he suspects that the proportion who come to get the free birthday gift is higher for younger (human) members. He collects a random sample from from a group of members ages 40+ years (older) and a group aged 20-39 years (younger), then compares data from the two age groups. He tests the following hypotheses using 𝛼 = 0.001 : H0: 𝑝 𝑜 𝑙 𝑑 𝑒 𝑟 − 𝑝 𝑦 𝑜 𝑢 𝑛 𝑔 𝑒 𝑟 = 0 HA: 𝑝 𝑜 𝑙 𝑑 𝑒 𝑟 − 𝑝 𝑦 𝑜 𝑢 𝑛 𝑔 𝑒 𝑟 < 0 He finds the following information, which is also available in the Excel sheet for this question. Proportion who get free birthday gift Sample size Older (40+ years) 0.14 150 Younger (20-39 years) 0.27 100 What is the test statistic for this hypothesis test? Answer to three decimal places. Show your calculations in your Excel file on the sheet for this question so that the instructor can award partial marks.
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