Sampling Distributions and Proportions

The video tutorial explains the process of election polling, focusing on sampling and calculating sample proportions. It introduces the concept of sampling distribution and how it relates to sample size. The tutorial covers confidence intervals, standard error, and margin of error, providing insights into their calculation and significance. It concludes with strategies to improve confidence intervals by increasing sample size.

Why is it not realistic to ask all 100,000 likely voters about their candidate preference?

• It is illegal to ask all voters.

• It is too time-consuming and expensive.

• Voters do not want to share their preferences.

• The results would be inaccurate.

What is the purpose of taking a sample from the population in statistics?

• To avoid asking the entire population.

• To estimate the population parameter.

• To reduce the number of voters.

• To increase the sample size.

What does the sampling distribution of sample proportions represent?

• The distribution of the entire population.

• The distribution of possible sample proportions.

• The distribution of the sample size.

• The distribution of the population parameter.

Under what condition can we assume the sampling distribution is roughly normal?

• When the true proportion is not too close to 0 or 1.

• When the sample proportion is exactly 0.5.

• When the sample size is less than 10% of the population.

• When the sample size is greater than 1000.

What is the mean of the sampling distribution of sample proportions?

• The standard deviation.

• The sample proportion.

• The population proportion.

• The sample size.

How do we estimate the standard deviation of the sampling distribution when the population proportion is unknown?

• By using the mean of the sample.

• By using the sample proportion.

• By using the sample size.

• By using the population size.

What is the formula for the standard error of the sample proportions?

• Square root of (n / (p * (1 - p)))

• Square root of (p * (1 - p) / n)

• Square root of (n / p)

• Square root of (p hat * (1 - p hat) / n)

What does a 95% confidence interval represent?

• The interval where the true population proportion lies 95% of the time.

• The interval where 95% of the sample proportions lie.

• The interval where the sample size is 95.

• The interval where 95% of the population lies.

How can the margin of error be reduced?

• By decreasing the confidence level.

• By decreasing the sample size.

• By increasing the sample size.

• By increasing the population size.

What is the relationship between sample size and margin of error?

• Larger sample size increases the margin of error.

• Larger sample size decreases the margin of error.

• Sample size does not affect the margin of error.

• Smaller sample size decreases the margin of error.