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 250 adults from this country and finds that 16 are vegetarian. Complete parts (a) through (c) below, . What is the sample proportion of vegetarians? - 60.064 (Round to three decimal places as needed.) b. What is Po, the hypothetical proportion of vegetariana? Po 0032 (Type an integer or a decimal. Do not round) c. Find the value of the best statistic. Explain the test statistic in context. z=(Round to two decimal places as needed.)

Answer 1

The sample proportion of vegetarians is 0.064, the hypothetical proportion is 0.032, and the test statistic is 1.509.

Step-by-step explanation:

The sample proportion of vegetarians can be calculated by dividing the number of vegetarians in the sample by the sample size. In this case, there are 16 vegetarians out of a sample size of 250, so the sample proportion is 16/250 = 0.064 (rounded to three decimal places).

The hypothetical proportion of vegetarians, Po, is given as 0.032 (rounded to three decimal places).

The value of the best statistic, the test statistic, can be calculated using the formula:

z = (sample proportion - hypothetical proportion) / sqrt(hypothetical proportion * (1 - hypothetical proportion) / sample size)

Substituting in the values, we have:

z = (0.064 - 0.032) / sqrt(0.032 * (1 - 0.032) / 250) = 0.032 / sqrt(0.03168 / 250) = 0.032 / 0.0212 = 1.509 (rounded to two decimal places).