Question

A certain survey is conducted by choosing randomly 10 students and asked them about the number of hours each of them spent on preparing for a final exam. The following are their answers to the question: 6,11,8,7,4,14,1,10,5,12

a- Construct the boxplot for the time spent studying for the exam.

b- Describe the distribution of the time spent studying for the exam

c- Find a 99% confidence interval for the mean time spent for studying

d- Interpret the confidence interval in (c).

Answer 1

Given:

A certain survey is conducted by choosing randomly 10 students and asked them about the number of hours each of them spent on preparing for a final exam.

The following are their answers to the question: 6,11,8,7,4,14,1,10,5,12 :

Arrange the given data in ascending order

1, 4, 5, 6, 7, 8, 10, 11, 12, 14

Five numbers summary :

Minimum = 1

First quartile, Q1 : first quartile is the median of the first half of the data

Q1 = 5

Median, Q2 = (7+8)/2 = 7.5

Third quartile, Q3 : Third quartile is the median of the second half of the data.

Q3 = 11

Maximum = 14

The boxplot for the time spent studying :

b) Since mean = 7.8 > median = 7.5, the distribution is positively skewed or skewed to right.

d) Interpretation :

We are 99% confident that the mean time spent for studying is between 3.70 and 11.90