At a large company banquet for several thousand employees and their families, many of the attendees became ill the next day. The company doctor suspects that the illness may be related to the fish, one of three options for the main course. Because all the dinner guests had to preorder their meal, the doctor was able to randomly select and contact 80 people that ate the fish, of which 64 people got sick. The doctor also randomly selected (and contacted) 60 people that did not eat the fish, of which 39 people got sick. The doctor also knows that at least 1000 attendees ordered the fish.

Required:
a. Is this convincing evidence that the true proportion of all attendees who ate the fish that got sick is more than the true proportion of all attendees who did not eat the fish that got sick?
b. Which mistake (a Type I error or a Type II error) could you have made? Interpret the potential error in context.

a. Yes. This provides convincing evidence that the true proportion of all attendees who ate the fish that got sick (80%) is more than the true proportion of all attendees who did not eat the fish that got sick.

b. The mistake here would have been the rejection of the Doctor's theory or hypothesis to the effect that more attendees who ate the fish got sick than those who did not eat the fish. This is a Type 1 error. A Type 1 error occurs when a null hypothesis is rejected when it is true. On the other hand, a Type II error occurs when the null hypothesis is accepted when it should be rejected. While a Type I error is equivalent to a false positive, a Type II error is equivalent to a false negative.

Step-by-step explanation:

Total number of attendees who ordered fish = 1,000

Sample size of the attendees who ate fish = 80

Number of attendees who ate the fish and got sick = 64 (80% or 64/80)

Sample size of attendees who did not eat fish = 60

Number of attendees who did not eat fish and got sick = 39 (65% or 39/60)

alokdubeyvidyaatech alokdubeyvidyaatech · Answer 2 · 2022-01-27T10:59:20+01:00

Part A: The given evidence is convincing to provide the true proportion regarding the attendees.

Part B: The error is a type 1 error in the hypothesis testing.

Type 1 Error and Type 2 Error

A type 1 error in hypothesis testing occurs when a null hypothesis is rejected when it is true.

A type II error in hypothesis testing occurs when the investigator fails to reject the null hypothesis that is actually false.

Given that, the total number of attendees who ordered fish is 1000. The random selection for the sample size of the attendees who ate fish is 80 of which 64 people got sick.

The number of attendees who ate the fish and got sick is calculated as given below.

No. of attendees =[tex]\dfrac {64}{80}[/tex]

% of No. of attendees = [tex]\dfrac {64}{80}\times 100[/tex]

% of No. of attendees = 80%

The random selection for the sample size of the attendees who did not eat fish is 60 of which 39 people got sick.

The number of attendees who did not eat the fish and got sick is calculated as given below.

No. of attendees = [tex]\dfrac {39}{60}[/tex]

% of No. of attendees =[tex]\dfrac {39}{60} \times 100[/tex]

% of No. of attendees = 65%

Part A

The given evidence is convincing to provide the true proportion of all attendees who ate the fish that got sick is more than the true proportion of all attendees who did not eat the fish that got sick.

Part B

The mistake here is that the doctor's theory (hypothesis) got rejected regarding the number of attendees who ate the fish got sick than those who did not eat the fish.

This error is a type 1 error in the hypothesis testing.

To know more about the type 1 and type 2 errors, follow the link given below.

https://brainly.com/question/20914617.