Teenagers send many text messages-recent polls cite medians of more than 50 per

Question

Teenagers send many text messages-recent polls cite medians of more than 50 per day. consider a large population of teenagers for whom the distribution of the number of text messages sent per day is strongly skewed to the right. Here is the five number summary for number of texts per day for this population Minimum = 0 Quartile 1=20 Median - 55 Quartile 3 = 140 Maximum = 250 Suppose we take random samples of size 32 from this population and calculate Q1 for each of our samples Below is a dotplot of Q1 from 50 such samples. Briefly explain what the dot at 35 represents Is the sample Q1 an unbiased estimator population Q1? Justify your answer.

Explanation / Answer

a. Briefly explain what the dot at 35 represents. (2pts) The dot at 35 represents the first quartile of one of the 50 samples taken from this population. b. Is the sample Q1 an unbiased estimator of the population Q1? Justify your answer. (3pts) We know from the five-number summary that the true population value of Q1 is 20. It appears that the distribution of the sample first quartiles is skewed right, but its median is 20, so it’s safe to say that the center of the distribution is near 20. Therefore the sample first quartile is an unbiased estimator.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.