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In: Statistics and Probability

In a nursing home study, researchers found that 12 out of 34 randomly selected small nursing...

In a nursing home study, researchers found that 12 out of 34 randomly selected small nursing homes had a resident vaccination rate of less than 80%m while 17 out of 24 randomly selected large nursing homes had a vaccination rate of less than 80%.

a. At an alpha of 0.05, test the claim that there is no difference in the proportions of the small and large nursing homes with a resident vaccination rate of less than 80%.

b. What is the 90% confidence level of the difference between proportions?

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