Understanding Confidence Intervals and Sample Size

Nadia aims to create a confidence interval to estimate the mean driving range of a new electric vehicle, with a margin of error no more than 10 km at a 90% confidence level. A pilot study suggests a standard deviation of 15 km. The video explores traditional and alternative methods for calculating the required sample size, using t-statistics and z-scores. The final calculation shows that a sample size of at least 7 is needed to achieve the desired margin of error.

What is the desired margin of error for Nadia's confidence interval?

• 15 kilometers

• 5 kilometers

• 10 kilometers

• 20 kilometers

Why is it challenging to determine the sample size using the t-statistic?

• Because the population mean is unknown

• Because the standard deviation is too large

• Because the degrees of freedom depend on the sample size

• Because the confidence level is too high

What alternative method is suggested for constructing a confidence interval?

• Using the chi-square distribution

• Using the z-score

• Using the F-distribution

• Using the binomial distribution

What standard deviation value is used from the pilot study?

• 10 kilometers

• 18 kilometers

• 12 kilometers

• 15 kilometers

Which function is used to calculate the z-score for a 90% confidence interval?

• Normal distribution

• Inverse norm

• Standard deviation

• Mean calculation

What is the approximate z-score value for a 90% confidence interval?

• 2.33

• 1.28

• 1.96

• 1.645

What is the first step in solving for the sample size algebraically?

• Multiply both sides by the z-score

• Divide both sides by the z-score and standard deviation

• Add the z-score to both sides

• Subtract the z-score from both sides

What is the smallest whole number sample size that satisfies the margin of error requirement?

• 7

• 8

• 6

• 5

Why is it important to use a whole number for the sample size?

• Because it simplifies calculations

• Because fractions are not allowed in statistics

• Because sample size must be a count of items

• Because it reduces the margin of error

What will Nadia need to verify after conducting her study?

• If the margin of error is within 10 kilometers

• If the confidence level was too low

• If the mean is exactly as predicted

• If the sample size was too large