Question

Question 5 Buying a year's worth of textbooks for college can be expensive! Consider a large population of college students for whom the distribution of the annual cost of textbooks is slightly skewed to the left. Here is the five-number summary for the annual cost of textbooks for this population: Minimum 80 Quartile 1 215 Median 335 Quartile 3380 Maximum 440 Suppose we take random samples of size 32 from this population and calculate the interquartile range (IQR) for each of our samples. Below is a dotplot of the IQR from 50 such samples. 60 80 100 120 140 160 180 200 220 240 280 Sample IQR A) Briefly explain what the dot at 240 represents. (3 points) B) Is the sample IQR is an unbiased estimator of the population IQR? Justify your answer.(5 points)

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Minimum 80

Quartile 1 (Q) 215

Median 335

Quartile 3 (Q3) 380

Maximum 440

Population IQR

IQR = Q3 - Q1 = 380 - 215 = 165

A.)

Dot at 240

The dot plot shows the sample distribution of interquartile range, hence, all the points on the plot represents the interquartile range for 50 different samples.

Hence, the dot at 240 represent the interquartile range value of one of the 50 sample distributions.

B.)

According to the sampling distribution chart, the graph form a bell shaped curve and loos fairly symmetric, hence we could conclude thatvthe mean IQR of the sampling distribution is about 165.

Since population IQR is also 165 ; we can conclude that sampling distribution OF IQR is an unbiased estimator of population IQR.