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# Descriptive Statiatics & Confidence Interval

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1. The figure below shows the probability histogram for the total number of spots when a die is rolled eight times. The shaded area represents the chance that the total will be between__ _ and ___ (inclusive).

8. A coin is tossed 100 times. True or false, and explain:
(a) The expected value for the number of heads is 50.
(b) The expected value for the number of heads is 50, give or take 5 or so.
(c) The number of heads will be 50.
(d) The number of heads will be around 50, give or take 5 or so.

Questions for Excel

The attached excel file contains measurements made on men involved in a physical fitness course at N.C. State University. The variables are age (years), weight (kg), oxygen intake rate (ml per kg body weight per minute), time to run 1.5 miles (minutes), heart rate while resting, heart rate while running (same time oxygen rate measured), and maximum heart rate recorded while running.

a. For the variables age and weight calculate their means and standard deviations
b. Determine whether these variables are approximately normally distributed.
c. For the variables age and weight calculate a 95% confidence interval for the mean.
d. Define a new variable that classifies individuals as 'old' or 'young' according to whether they are below or above 43 years old. Then calculate means, standard error and a 95% confidence interval for the mean time to run 1.5 miles for both the young and the old individuals. Do they seem different to you?

https://brainmass.com/statistics/confidence-interval/descriptive-statistics-confidence-interval-429377

#### Solution Preview

1. The figure below shows the probability histogram for the total number of spots when a die is rolled eight times. The shaded area represents the chance that the total will be between_20 _ and _25_ (inclusive).

8. A coin is tossed 100 times. True or false, and explain:
(a) The expected value for the number of heads is 50.
True
Expected value for the number of heads = np = 100 * ½ = 50
(b) The expected value for the number of heads is 50, give or take 5 or so.
False
Expected value = 50 and is fixed for 100 tosses of the coin.
(c) The number of heads will be 50.
False
P (getting a head), p = 1/2 = 0.5
P (the number of heads will be exactly 50) =
= 0.0796 = 7.96%
That is, the chance of getting exactly 50 heads in 100 tosses is only 7.96%.
(d) The number of heads will be around 50, give or take 5 or so.
False
Mean number of heads = np = 100 * ½ = 50
Standard deviation, σ = = 5
Thus the statement states that the number of heads will be within 1 standard deviation of the mean.
Empirical rule states that for a normal distribution,
About 68% (precisely 68.27%) of the values lie within 1 standard deviation of the mean (or between the mean minus 1 times the standard deviation, and the mean plus 1 times the standard deviation).
That is, only 68% of the cases lie between 45 and 55.
Questions for Excel
The attached excel file contains measurements made on men involved in a physical fitness course at N.C. State University. The variables are age (years), weight (kg), oxygen intake ...

#### Solution Summary

The solution provides step by step method for the calculation of descriptive statistics and confidence interval for population mean. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

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