Understanding Bernoulli Distribution and Sampling

The video tutorial explains a hypothetical election scenario to introduce the concept of Bernoulli Distribution. It discusses how to estimate the probability of an event using sampling and surveys. The tutorial covers calculating sample mean and variance, understanding sample variance, and introduces confidence intervals to estimate the true mean of a population.

In the context of the election scenario, what does a Bernoulli Distribution represent?

• A distribution with no outcomes

• A distribution with exactly two possible outcomes

• A distribution with more than two outcomes

• A distribution with continuous outcomes

Why is it impractical to survey all 100 million people in the country?

• All of the above

• Because it is time-consuming

• Because it is impossible to reach everyone

• Because it is too expensive

What is the sample mean if 57 people vote for candidate A and 43 for candidate B?

• 0.50

• 0.57

• 0.43

• 0.60

How is the sample variance calculated in this scenario?

• By dividing the sum of distances by the number of samples minus one

• By dividing the sum of squared distances by the number of samples

• By dividing the sum of distances by the number of samples

• By dividing the sum of squared distances by the number of samples minus one

What does the standard deviation of the sampling distribution represent?

• The spread of the sample variance

• The spread of the sampling distribution of the sample mean

• The spread of the population distribution

• The spread of the sample distribution

How is the standard deviation of the sampling distribution estimated?

• By using the population variance

• By using the sample variance

• By using the sample standard deviation divided by the square root of the sample size

• By using the population standard deviation

What is the purpose of calculating a confidence interval?

• To determine the variance of the sample

• To find the exact mean of the population

• To calculate the standard deviation of the population

• To estimate the range in which the true mean of the population lies with a certain level of confidence

What does a 95% confidence interval imply?

• The true mean is definitely within the interval

• There is a 95% chance that the true mean is within the interval

• The sample mean is within the interval

• The variance is within the interval

Why is it important to remember that the standard deviation estimate is just an estimate?

• Because it is always accurate

• Because it is irrelevant to the mean

• Because it can change with different samples

• Because it is not used in calculations

What is the relationship between the sample mean and the population mean in this context?

• The sample mean is always greater than the population mean

• The sample mean is always less than the population mean

• The sample mean is an estimate of the population mean

• The sample mean is unrelated to the population mean