Subjects were asked to taste two wine samples in sequence.

Both samples given were the same wine although subjects were expecting to taste two different samples.
Of the 32 subjects in the study, 22 selected the wine presented first when presented with two identical samples.

A) Give a 95% confidence interval for the proportion of subjects who would select the first choice presented.

B) Subjects were recruited in Ontario, Canada via advertisements. What assumption are you making about these subjects?

Please help. I have no clue. Thank you.

A) To calculate a confidence interval for the proportion of subjects who would select the first choice presented, we can use the formula for a confidence interval for a proportion:

CI = p̂ ± Z * √((p̂(1-p̂))/n)

Where:
- p̂ is the sample proportion (in this case, the proportion of subjects who selected the first choice)
- Z is the Z-score corresponding to the desired confidence level (in this case, 95% confidence level)
- n is the sample size (in this case, the total number of subjects)

To calculate the confidence interval, we need to find the sample proportion (p̂), which is calculated by dividing the number of subjects who selected the first choice by total subjects.

Given that 22 out of 32 subjects selected the first choice:

p̂ = 22/32 = 0.6875

To find the Z-score for a 95% confidence level, we can refer to the standard normal distribution table or use a statistical calculator. The Z-score for a 95% confidence level is approximately 1.96.

Substituting these values into the formula, we get:

CI = 0.6875 ± 1.96 * √((0.6875 * (1-0.6875))/32)

Simplifying the calculation, we can find the confidence interval.

B) Based on the information provided, we can assume that the subjects recruited in Ontario, Canada via advertisements are representative of the larger population. This assumption is crucial for generalizing the study's findings to the entire population of interest. In other words, we assume that the characteristics and preferences of the subjects in the study reflect the characteristics and preferences of the broader population in Ontario, Canada. However, this assumption may not always hold true, as there could be factors that introduce bias into the sampling process, such as self-selection bias or non-response bias. It's always important to acknowledge the potential limitations and biases in any study based on its recruitment methods.