Statistics for Data Science and Business Analysis - Calculating Confidence Intervals Within a Population with a Known Va

Why is it often necessary to use sample data instead of population data?

• Population data is always accurate.

• Sample data is more reliable.

• Population data is often too large to analyze.

• Sample data is easier to manipulate.

What is a key assumption when calculating confidence intervals with a known variance?

• The sample size must be small.

• The population is normally distributed.

• The sample mean is zero.

• The variance is unknown.

In the example provided, what is the standard deviation of data science salaries?

• $15,000

• $10,000

• $25,000

• $20,000

What does a 95% confidence interval imply about the population parameter?

• It will never fall within the interval.

• It has a 95% chance of falling within the interval.

• It will definitely fall within the interval.

• It has a 5% chance of falling within the interval.

What is the critical value for a 95% confidence interval in the example?

• 2.58

• 2.33

• 1.96

• 1.64

How does increasing the confidence level to 99% affect the confidence interval?

• It makes the interval narrower.

• It makes the interval broader.

• It makes the interval more precise.

• It does not change the interval.

What is the trade-off when choosing a higher confidence level?

• Higher confidence leads to a narrower interval.

• Higher confidence leads to a broader interval.

• Higher confidence increases precision.

• Higher confidence decreases the sample size.