Question

**WILL FAN & MEDAL**
A university is conducting a survey to study the number of hours students sleep at night during exam week. A sample of 20 students was drawn, and these responses were obtained: 6.5, 5, 8, 5.5, 7, 4, 4.5, 5, 6, 5.5, 4, 7.5, 6, 7, 8, 5, 6, 6.5, 6.5, 5. The standard deviation of the population mean is 2 hours.

Arrange the steps in the correct sequence to find the range in which 95% of the sample mean occurs.
**Step choices are below**

Answer 1

1) The range in which 95% of the sample mean occurs
=5.93+2 x 0.45 and 5.93-2 x 0.45
=6.83 hours and 5.03 hours

2) The sample mean is \[\mu=\frac{ 118.5 }{ 20 }=5.93\]

3) calculate the standard deviation

4) the 20 students' total number of study hours is 118.5 hours

5) The standard error of the mean of the sample is \[\frac{ \sigma }{ \sqrt{N} }=\frac{ 2 }{ \sqrt{20} }=0.45\]

6) the range in which 95% of the sample mean occurs is \[\mu \pm2 \times \frac{ \sigma }{ \sqrt{N} }\]

Answer 2

@mathmale do you understand this?