Ch.7 # 14
Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking—even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually)b in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights no and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycle at the end of the study was as follows: 25, 27, 25, 23, 24, 25, 26, and 25.

Using the 5% level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from the 24 hours?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved. (c) Explain your answer to someone who has never taken a course in statistics. Solution:

(a) Use the steps of hypothesis testing.
Size of sample, n = 8
Degree of freedom = n-1 = 8-1 = 7
Sum of sample = i=1∑n=8xi = (25+27+25+23+24+25+26+25) = 200 | Time (in Hours)| Sum| Mean(xm)| (xi- xm)2| Standard Deviation| 1| 25| 200| Mean = Sum/n= 200/8= 25| 0| σ = √( i=1∑n=8(xi-xm)2/(n-1))= √(10/7)= √1.4285= 1.195| 2| 27| | | 4| |

Here X = 25
σ = 1.195
We can define two-tailed statistics for above observations as follows: Null Hypothesis: H0: =24 vs. Ha: 24
Rejection region:
z < -z/2 or z > z/2
Here significance level is 0.05,
So, z0.025 = 1.96 (Using Statistical Ratio Calculator
Now,
z = (X - μ) / σx
Where X is a normal random variable, μ is the mean, and σ is the standard deviation.

...Summary StatisticsMean
88.532
Std Dev
5.0794269
Std Err Mean
0.2271589
Upper 95% Mean
88.978306
Lower 95% Mean
88.085694
N
500
Sum
44266
Summary StatisticsMean
97.103333
Std Dev
5.0448811
Std Err Mean
0.2912663
Upper 95% Mean
97.676525
Lower 95% Mean
96.530142
N
300
Sum
29131...

...Air Force Assignment
1. Use appropriate descriptive statistics to summarize the training time data for each method. What similarities or differences do you observe from the sample data?
Descriptive analysis in excel has been used to come up with relevant figures of the given data samples which is tabulated below:
Descriptive Statistics | Current | Proposed |
Mean | 75.06557 | 75.42623 |
Standard Error | 0.505094 | 0.32091 |
Median | 76 |...

...Trajico, Maria Liticia D.
BSEd III-A2
REFLECTION
The first thing that puffs in my mind when I heard the word STATISTIC is that it was a very hard subject because it is another branch of mathematics that will make my head or brain bleed of thinking of how I will handle it. I have learned that statistic is a branch of mathematics concerned with the study of information that is expressed in numbers, for example information about the number of times...

...the sample mean and the original.
The z score represents the distance of each X or score from the mean.
If the distance between the sample mean and the population mean the z score will
increase.
b) Increasing the population standard deviation.
The standard deviation is the factor that is used to divide by in the equation. the bigger the SD,
then the smaller the z score.
c) Increasing the number of scores in the sample.
Should...

...Statistics 1
Business Statistics
LaSaundra H. – Lancaster
BUS 308 Statistics for Managers
Instructor Nicole Rodieck
3/2/2014
Statistics 2
When we hear about business statistics, when think about the decisions that a manager makes to help make his/her business successful. But do we really know what it takes to run a business on a statistical level? While some may think that business...

...
MBA 501A – [STATISTICS]
ASSIGNMENT 4
INSTRUCTIONS: You are to work independently on this assignment. The total number of points possible is 50. Please note that point allocation varies per question. Use the Help feature in MINITAB 16 to read descriptions for the data sets so that you can make meaningful comments.
[10 pts] 1. Use the data set OPENHOUSE.MTW in the Student14 folder. Perform the Chi
Square test for independence to determine whether style of home and...

...1. Introduction
This report is about the case study of PAR, INC. From the following book: Statistics for Business an Economics, 8th edition by D.R. Anderson, D.J. Sweeney and Th.A. Williams, publisher: Dave Shaut. The case is described at page 416, chapter 10.
2. Problem statement
Par, Inc. has produced a new type of golf ball. The company wants to know if this new type of golf ball is comparable to the old ones. Therefore they did a test, which consists out of 40...

...10, 2012
1. Multiple and True/False Questions (10 points) Please circle the right answer for the questions below. Each question is assigned 2.5 points.
1. The sample mean of population 1 is smaller than that of population 2. If we are interested in testing whether the mean of population 1 is significantly smaller than the mean of population 2, the a. null hypothesis should state µ1 − µ2 < 0 b. null hypothesis should state µ1 − µ2 ≤ 0 c....

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