Question

directions: examine the data sets given in the problems below and answer their corresponding questions.

1. the university of texas is interested in determining the average number of hours of sleep a pre - med major gets each night. they surveyed eight random individuals. the data is shown below:

individual	a	b	c	d	e	f	g	h

a. calculate the mean number of hours of sleep for this sample.

b. the standard deviation for this sample is 1.07 hrs.

c. calculate the standard error of the mean for this sample (remember, once calculated multiply by 2 to get +/- 2 sem). this is your 95% confidence interval, also known as an error bar.

d. use the space provided to make a bar graph for the mean number of hours slept and include an error bar.

sleep study of pre - med majors

mean hours of sleep

university of texas sample

e. harvard heard about the study being conducted by the university of texas and decided to replicate it. the data is shown below. without doing calculations, predict whether the data gathered by harvard will have a higher or lower standard deviation than that of the university of texas. why?

individual	a	b	c	d	e	f	g	h

f. optional bonus: now calculate the standard deviation for the data gathered by harvard (in excel or on your calculator). does it match your prediction?

Explanation:

Part a

Step1: Sum the data values

The data values are 6, 4, 7, 7, 6, 5, 7, 6. Sum them: \(6 + 4 + 7 + 7 + 6 + 5 + 7 + 6 = 48\)

Step2: Divide by the number of data points

There are 8 data points. Mean \(=\frac{48}{8}=6\)

Step1: Recall the formula for standard error of the mean (SEM)

The formula for SEM is \(\text{SEM}=\frac{s}{\sqrt{n}}\), where \(s\) is the sample standard deviation and \(n\) is the sample size.

Step2: Substitute the values

Given \(s = 1.07\) and \(n = 8\). First, calculate \(\sqrt{8}\approx2.828\). Then \(\text{SEM}=\frac{1.07}{2.828}\approx0.378\). Multiply by 2 for \( \pm 2\text{SEM}\): \(2\times0.378\approx0.756\) (or using the SEM first: \(\text{SEM}=\frac{1.07}{\sqrt{8}}\approx0.378\), and \(2\times\text{SEM}\approx0.76\) (rounded))

Standard deviation measures the spread of data. The Harvard data has values (3, 5, 7, 8, 6, 11, 2, 12) which are more spread out (ranging from 2 to 12) compared to the Texas data (ranging from 4 to 7). A larger spread means a higher standard deviation.

Answer:

The mean number of hours of sleep is 6.

Part c