6.100

Question 1. From a population P, 500 students were polled at random for how many minutes they spend on Instagram each day. The average of their responses is 135 minutes, with a 95% confidence interval of +/-5 minutes. Assume that each student would give the same response if they were polled again.

Which of the following could we infer? Check all that apply.

About five percent of the students polled (about 25 individuals) reported either less than 130 minutes or more than 140 minutes.

A student randomly sampled from P is equally likely to report any duration between 130 and 140 minutes.

A student randomly sampled from P has less than a 10% chance of reporting more than 140 minutes.

If another sample of 500 students were taken from P, there is a 95% chance that the average of their responses would be between 130 and 140 minutes.

If another sample of 500 students were taken from P, a 95% confidence interval for their average response would likely have a width similar to +/-5 minutes.

If another sample of 1000 students were taken from P, a 95% confidence interval for their average response would lie entirely within the interval [130, 140] minutes.

Question 2. Which of the following are true? Check all that apply.

A p-value of p means there is p probability that the null hypothesis is true.

A p-value of p means there is 1 - p probability that the null hypothesis is true.

Consider the hypothesis that sharks swim faster than dolphins. If we were able to find all sharks and dolphins in the world and measure each of their top speeds, we could calculate a probability 0 < p < 1 (non-inclusive range) on whether the average shark speed is greater than the average dolphin speed.

Because we can't track down every shark and dolphin, we sample from their populations and measure their individual speeds. Out of our sample, we find sharks have an average speed of 26 m/s, and dolphins have an average of 23 m/s. After running a permutation test on our hypothesis, we find that in two percent of the permuted samples, the "shark" group's average was at least 3 m/s greater than the "dolphin" group's. Hence, we can conclude there is a 98% chance that on average, sharks swim faster than dolphins.

Lecture 10 Finger Exercise