Question

Naomi works at a doctor's office. She surveyed a random sample of 100 patients and found that 70% of the patients surveyed take a daily vitamin. Naomi wanted to know if it is plausible that 75% of the entire population of the doctor's patients take a daily vitamin. Naomi performed 360 trials of a simulation. Each trial simulated a sample of 100 patients under the assumption that 75% of the population takes a daily vitamin. The dot plot shows the results of the simulations.

What is the best conclusion for Naomi to make based on the data?

a) It is not plausible that 75% of the population takes a daily vitamin because the data shows that a sample proportion of 70% is unlikely.

b) It is plausible that 75% of the population takes a daily vitamin because the data shows that a sample proportion of 70% is fairly likely.

c) It is not plausible that 75% of the population takes a daily vitamin because the data shows that a sample proportion of 70% is fairly likely.

d) It is plausible that 75% of the population takes a daily vitamin because the data shows that a sample proportion of 70% is unlikely.

Answer 1

Naomi can conclude that it is plausible 75% of the population takes a daily vitamin if the dot plot from her simulations commonly shows a sample proportion of 70%.

Step-by-step explanation:

The best conclusion Naomi can make based on the simulation data is option b) It is plausible that 75% of the population takes a daily vitamin because the data shows that a sample proportion of 70% is fairly likely. This conclusion is supported if the dot plot indicates that a result of 70% is within the range of common outcomes when assuming that the true proportion of the population that takes a daily vitamin is 75%. If the dot plot shows that 70% is a frequent result of the simulations, it means that obtaining a sample proportion of 70% would not be unusual, and thus, the hypothesis that 75% of the entire patient population takes a daily vitamin is plausible.