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A study is conducted to assess whether residents in City A spent a different out-of-pocket amount...

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Statistics

A study is conducted to assess whether residents in City A spenta different out-of-pocket amount on prescription medications fromresidents in City B last year. The study is restricted to residentswho are 50 years of age or older. Residents are selected at random.For each resident, the total amount of dollars spent onprescription medications over the last year is recorded. Thesummary statistics of the sample data are given in the table below.Let µ1 be the mean out-of-pocket amount that residents in City Aspent, and µ2 be the mean out-of-pocket amount that residents inCity B spent. Run a two-sample t-test assuming equal variances. Usea significance level of 0.05. City Sample size Sample mean Samplestandard deviation A 37 421 37 B 55 380 39

a. Write down the null hypothesis.

b. Write down the alternative hypothesis.

c. Calculate the point estimate for µ1 − µ2. (5 points) d.Calculate the pooled sample variance.

e. Calculate the standard error of the point estimate in c. (10points) f. Calculate the test statistic. (10 points) g. Find outthe critical value.

h. Is there a statistically significant difference in theout-of-pocket amount spent on prescription medications between CityA and City B?

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