Question

Nkechi wants to use a one-sample z interval to estimate what proportion of candies in a bag are red. She takes a random sample of 24 of the 80 total candies and finds that 18 of the candies in the sample are red. Which conditions for constructing this confidence interval did Nkechi's sample meet? Choose all answers that apply

Answer 1

Nkechi's sample meets the conditions for a one-sample z interval for a proportion, including randomness, at least 10 successes and failures, and a sample size less than 10% of the population.

Step-by-step explanation:

The student's question pertains to whether the conditions for constructing a one-sample z interval for a proportion have been met. Nkechi's sample would meet several conditions:

• The sample is random.
• There are at least 10 successes (18 red candies) and 10 failures (24 - 18 = 6 non-red candies).
• The sample size is less than 10% of the population (24 is less than 10% of 80, so sampling without replacement is okay).

It appears that Nkechi meets the necessary conditions for constructing a confidence interval for the proportion of red candies using a one-sample z interval.

Answer 2

Answer: The data is a random sample from the population of interest.

Step-by-step explanation: The condition is met since she randomly selected the sample from the population of interest.