Management of a company that operates a nationwide network of pharmacies is inte

Question

Management of a company that operates a nationwide network of pharmacies is interested in offering the flu vaccine (the "flu shot") in its stores. Before the company invests in the necessary supplies and training, it wants to estimate the size of its potential market. After collecting data from a survey of 200 randomly selected customers, the company found that 96 of them reported that they get the flu shot every year (from some other provider, e.g., a doctor or another pharmacy). The company used this information to calculate a 95% confidence interval, obtaining the endpoints 0.411 and 0.549.

Which of the following statements correctly interprets this interval in the context of the problem?

The company can be 95% confident, based on the method used to calculate the interval, that the proportion of customers in the sample of 200 who get the flu shot every year is between 0.411 and 0.549. That is, between 41.1% and 54.9% of this group of 200 customers get the flu shot.

The company can be 95% confident, based on the method used to calculate the interval, that the proportion of repeated samples of 200 customers that would contain the population proportion of customers who got the flu shot, 0.48, is between 0.411 and 0.549. That is, between 41.1% and 54.9% of repeated samples would contain the true population proportion of vaccinated customers, which was found to be 48%.

The company can be 95% confident, based on the method used to calculate the interval, that 95% of its customers fall in the interval between 0.411 and 0.549. That is, the company has between 41.1% and 54.9% of the flu vaccine market.

The company can be 95% confident, based on the method used to calculate the interval, that the true proportion of all customers who get the flu shot every year is between 0.411 and 0.549. That is, between 41.1% and 54.9% all customers get the flu shot each year.

The company can be confident, based on the method used to calculate the interval, that 95% of the time, the proportion of customers who will report that they get the flu shot every year is between 0.411 and 0.549. That is, 95% of the time, between 41.1% and 54.9% of customers get the flu shot every year.

The company can be confident, based on the method used to calculate the interval, that there is a 95% chance that a randomly selected customer has received between 41.1% and 54.9% of the recommended vaccines, according to the CDC.

The company can be 95% confident, based on the method used to calculate the interval, that the proportion of customers in the sample of 200 who get the flu shot every year is between 0.411 and 0.549. That is, between 41.1% and 54.9% of this group of 200 customers get the flu shot.

The company can be 95% confident, based on the method used to calculate the interval, that the proportion of repeated samples of 200 customers that would contain the population proportion of customers who got the flu shot, 0.48, is between 0.411 and 0.549. That is, between 41.1% and 54.9% of repeated samples would contain the true population proportion of vaccinated customers, which was found to be 48%.

The company can be 95% confident, based on the method used to calculate the interval, that 95% of its customers fall in the interval between 0.411 and 0.549. That is, the company has between 41.1% and 54.9% of the flu vaccine market.

The company can be 95% confident, based on the method used to calculate the interval, that the true proportion of all customers who get the flu shot every year is between 0.411 and 0.549. That is, between 41.1% and 54.9% all customers get the flu shot each year.

The company can be confident, based on the method used to calculate the interval, that 95% of the time, the proportion of customers who will report that they get the flu shot every year is between 0.411 and 0.549. That is, 95% of the time, between 41.1% and 54.9% of customers get the flu shot every year.

The company can be confident, based on the method used to calculate the interval, that there is a 95% chance that a randomly selected customer has received between 41.1% and 54.9% of the recommended vaccines, according to the CDC.

Explanation / Answer

Correct answer:

d. The company can be 95% confident, based on the method used to calculate the interval, that the true proportion of all customers who get the flu shot every year is between 0.411 and 0.549. That is, between 41.1% and 54.9% all customers get the flu shot each year.

Explanation:

We know that the confidence interval for the population proportion gives us the estimates for the lower and upper bound for the population proportion based on the sample proportion and confidence level. A true proportion of all customers who get the flu shot every year is nothing but the population proportion.

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