# Histogram & Blood Sugar Tracking Statistics Discussion Help

*label*Mathematics

*timer*Asked: Feb 17th, 2019

*account_balance_wallet*$20

### Question Description

Choose two of your classmates’ data sets. Take 30 random samples of 5 data points each (one way: Paste the data here http://www.randomizelist.com/ randomize the list and take the first 5 numbers, or use the sampling feature at http://www.statpowers.com/descriptiveStats.html), and calculate the average for each of these samples. You will now have 30 sample means. Create and post a histogram for your sample means. What is the mean of these means? What is the standard deviation? Does this make sense based on the Central Limit Theorem? Do the sample means follow a normal distribution? What p-value does the normality test give? How and why does this differ from the original data?

person 1

Data: Heartrates (in beats per minute) for 30 patients

Sample Mean: 70.9

Standard Deviation: 6.79

Histogram: provided in attachment

The data does seem to follow the bell curve of normal distribution

person 2 I used my chart from January blood sugars. When I put the numbers into the Shapiro-Wilk test, it seemed to follow the normal distribution. The results are below:

n = 12 Mean = 79.75 SD = 13.410477586234917 W = 0.939565955711239 Threshold (p=0.01) = 0.8050000071525574 --> HO accepted Threshold (p=0.05) = 0.859000027179718 --> HO accepted Threshold (p=0.10) = 0.8830000162124634 --> HO accepted

## Tutor Answer

Attached.

1

Student Name

Professor Name

Course Name

18 February 2019

Discussion Responses

Person 1:

For this study, 30 random samples of 5 data points each were taken from the "Heart Rate"

data set. The average for each of the 30 samples was calculated and a histogram was created as

follows:

Figure 1. Sample Means Histogram

Sample Means Histogram

9

8

8

8

7

6

6

5

5

4

3

3

2

1

0

Bin 1 (67-68)

Bin 2 (69-70)

Bin 3 (71-72)

Bin 4 (73-74)

Bin 5 (75-77)

The average for the 30 means was found to be 71,32667, and the standard deviation

2,357955. Based on the Central Limit Theorem, which says that the average of a large number of

independent observations (themselves not necessarily normal) is normal, this makes sense (the

histogram also says so by its shape). Also, the sample means follow a normal distribution, as

2

indicated by the Shapiro-Wilk test, with a p-value for the 0,05 significance threshold of 0,9269.

This did not differ from the original data where the...

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