Question

In: Statistics and Probability

Through March 16th of this year, 12% of patients in the United States who had contracted...

Through March 16th of this year, 12% of patients in the United States who had contracted COVID-19 were hospitalized (Centers for Disease Control). In Orange County, Florida, as of April 8, 2020, out of 931 confirmed COVID-19 cases, there were 129 hospitalizations (The Orange County Register). Use this sample information to conduct a test of significance to determine whether the rate of hospitalization due to COVID-19 in Orange County is greater than the rate of hospitalization in the United States population.

  1. State the null and alternative hypotheses.
  2. What test will you use? ____________________________Check the assumptions and conditions. Note any concerns you might have that would call the conclusion of the test into question.

Solutions

Expert Solution

In this case, testing the rate of hospitalization is equivalent to testing the proportion of hospitalization cases.

Let p be the proportion of hospitalization cases in Orange county.

The null hypothesis (H0) and alternative hypothesis (H1) are given by,

We have to test, H0: p = 0.12 against H1: p > 0.12

The one proportion t-test needs to be performed.

The test-statistic is given by, Z = , where, = 129/931 = 0.1386, = 0.12, n = 931

Thus, Z = 1.7464

Under H0, Z ~ N(0,1)

If we assume 5% level of significance, then the critical value is = = 1.64

Since, observed Z > 1.64, we reject H0.

We conclude at 5% leve of significance, there is enough evidence to claim that the proportion or rate of hospitalization is higher in Orange county.

orchestra answered 2 years ago
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