A recent national survey indicated that 73 percent of respondents try to include locally grown foods in their diets. A 95 percent confidence interval for the proportion of all people in the country who try to include locally grown foods in their diets is given as (0.70,0.76). Assume all conditions for inference were met. Based on the confidence interval, which of the following claims is supported

A Less than half of all people in the country try to include locally grown foods

Less than 70 percent of all people in the wywy to include loc us than 75 percent of all people in the country by to nclude

Less than 10 percent of all people in the country wy to include

At least 2 percent of all people in the co confidence at the proportion of 9

Question

Mathematics

Nelson Hayes

13 November, 15:03

A recent national survey indicated that 73 percent of respondents try to include locally grown foods in their diets. A 95 percent confidence interval for the proportion of all people in the country who try to include locally grown foods in their diets is given as (0.70,0.76). Assume all conditions for inference were met. Based on the confidence interval, which of the following claims is supported

A Less than half of all people in the country try to include locally grown foods

Less than 70 percent of all people in the wywy to include loc us than 75 percent of all people in the country by to nclude

Less than 10 percent of all people in the country wy to include

At least 2 percent of all people in the co confidence at the proportion of 9

+2

Answers (2)

Know the Answer?

Immanuel Ibarra · Answer 1

Less than 80 percent of all people in the country try to include locally grown foods in their diets.

Izabella Berry · Answer 2

Correct option is:

"Less than 75% of all people in the country try to include locally grown foods in their diets."

Step-by-step explanation:

A hypothesis for the proportion of people who include locally grown foods in their diets can be defined as:

H₀: The proportion of people who include locally grown foods in their diets is p.

Hₐ: The proportion of people who include locally grown foods in their diets is difference from p.

The decision rule can be based on the 95% confidence interval.

If the confidence interval consists the hypothetical value of the true proportion then the null hypothesis will be accepted or else the null hypothesis will be rejected.

The 95% confidence interval for the proportion of all people in the country who try to include locally grown foods in their diets is given as (0.70, 0.76).

This interval implies that there is 0.95 probability that the true proportion of people who include locally grown foods in their diets is between 70% and 76%.

Assuming that the claim made was supported by the 95% confidence interval.

The claim should be:

Less than 75% of all people in the country try to include locally grown foods in their diets.

Because the 95% confidence interval defines the range of the true proportion as 70% to 76%. Most of the values are below 75%.

Thus, the correct option is:

"Less than 75% of all people in the country try to include locally grown foods in their diets."