Quiz-6

Short answer solutions

Question: Suppose a researcher calculated a t-statistic which resulted in a p-value of 0.231. The sample size for the study was n = 500. Would you expect very similar, or different results if a z-test was performed using the exact same data? Justify your answer.

Answer: You would expect the results to be very similar (almost identical). This is because the shape of a t-distribution approaches a standard normal distribution as n increases. Our typical rule is that if our sample size is larger than 30, the results will be almost identical.

Question: In class, and in the assigned exploration, we simulated a bootstrap resample distribution to calculate a 95% confidence interval for the true mean bill length (in mm) of Penguins on the Palmer Islands.

In the context of the problem and in as much detail as possible, describe how one observation on this bootstrap resampled distribution was created.

Answer: We would randomly sample with replacement 344 (sample size) times from the original data set. Next, we would calculate the new sample mean. This sample mean is one dot on the simulated sampling distribution.