Question

in 2016 a poll estimated that 3.2​% of adults in a certain country are vegetarian. a nutritionist thinks this rate has changed. the nutritionist samples 300 adults from this country and finds that 16 are vegetarian. what is p^ the sample proportion of vegetarians?

Answer 1

The sample proportion of vegetarians in the nutritionist's study of 300 adults, out of whom 16 were found to be vegetarian, is 5.33%.

Step-by-step explanation:

Calculating the Sample Proportion of Vegetarians

To calculate the sample proportion (p') of vegetarians, we use the formula given in section 8.3 of your textbook:

p' = x/n, where x represents the number of successes (vegetarians in this case), and n represents the sample size.

A nutritionist sampled 300 adults and found that 16 are vegetarian. Using the formula, we calculate the sample proportion as follows:

p' = 16/300

We can simplify this to p' = 0.0533 (rounded to four decimal places), or 5.33%, which is the sample proportion of vegetarians in the nutritionist's study.

This sample proportion can be used, for instance, in hypothesis testing to compare against the previously estimated proportion of 3.2% to determine if there has been a statistically significant change in the vegetarian rate among adults in the country since 2016.