Question

Broome county’s health department hires you to analyze data on COVID-19. They come to you with data from your county’s local hospitals, and tell you that they have randomly tested 147 people showing symptoms of coronavirus. Results showed that 68 of those were positive for the virus. They are worried about running out of room in their hospitals, so they want you to estimate the true proportion of people with the virus.

The county officials are saying that based on initial results they believe about 46.3% of their county could have COVID-19. Explain to them why this is incorrect by defining the point estimate in this scenario and the parameter it is estimating.

Answer 1

Answer:

Given that,

Broome county’s health department hires you to analyze data on COVID-19. They come to you with data from your county’s local hospitals, and tell you that they have randomly tested 147 people showing symptoms of coronavirus. Results showed that 68 of those were positive for the virus.

They are worried about running out of room in their hospitals, so they want you to estimate the true proportion of people with the virus.

The county officials are saying that based on initial results they believe about 46.3% of their county could have COVID-19.

Explain to them why this is incorrect by defining the point estimate in this scenario and the parameter it is estimating:

The sample proportion is computed as follows, based on the sample size N=147 and the number of favorable cases X=68.

=68/147

=0.463

Therefore, =0.463

The critical value for =0.1 is . The corresponding confidence interval is computed as shown below:

Therefore, the Confidence interval is (0.3954, 0.5306).