LC2_2023 - Statistical Inference

What is the correct interpretation of a confidence interval for a significance level of α=0.05?

• If we take 100 samples and calculate the mean and confidence interval for each one of them, then the true population mean would be included in 95% of these intervals.

• If we take 100 samples and calculate the mean and confidence interval for each one of them, then the true population mean would be included in 5% of these intervals.

• If we take 100 samples and calculate the mean and confidence interval for each one of them, then the true population mean would be included in 100% of these intervals.

• For a given sample, there is a 95% chance that the true population mean lies within the confidence interval.

Which statements regarding standard error are TRUE?

• There is no connection between the standard deviation and the standard error.

• The standard error is a function of the sample size and the standard deviation.

• The standard error of the mean decreases as the sample size increases.

• The standard error of the mean increases as the standard deviation increases.

• None of these

• None of these

Which of the following do you need to compute a confidence interval around a sample mean?

• The critical value of the test statistic given a certain level of confidence

• A continuous variable (i.e., at least measured at the interval level)

• The sample mean

• The standard error

• None of these

What is the correct definition for the confidence interval?

• None of these

As a marketing manager at Spotify you wish to find the average listening time of your users. Based on a random sample of 180 users you found that the mean listening time for the sample is 7.34 hours per week and the standard deviation is 6.87 hours.

What is the 95% confidence interval for the mean listening time (the corresponding z-value for the 95% CI is 1.96)?

• [6.34; 8.34]

• • [7.15; 7.55]

• [6.25; 8.15]

• [6.54; 8.54]

• None of these

How can you compute the standardized variate of a variable X?

For a variable that follows a normal distribution, within how many standard deviations of the mean are 95% of values?

• 1.960

• 1.645

• 2.580

• 3.210