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.

...1033,5.04488)
Normal(107.15,5.15367)
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
Summary StatisticsMean
107.15
Std Dev
5.1536687
Std Err Mean
0.3644194
Upper 95% Mean
107.86862
Lower 95% Mean
106.43138
N
200
Sum
21430
From the table above, the total number of passengers for route 1 is 44,266, route 2 is 29,131 and route 3 is 21,430 and the total numbers of passengers for 3 routes are 94,827.
Although route 1 has the highest number of passengers and flights but it has the lowest means of passengers among the 3 routes. From the sample of 1000 flights, route 1 has 500 flights which carries a sample mean of 88.532 passengers; route 2 has 300 flights which carries a sample mean of 97.103 passengers and route 3 has 200 flights which carries a sample mean of 107.15 passengers. Hence the...

...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 | 76 |
Mode | 76 | 76 |
Standard Deviation | 3.944907 | 2.506385 |
Sample Variance | 15.5623 | 6.281967 |
Kurtosis | -0.06933 | 0.58694 |
Skewness | -0.22053 | -0.28749 |
Range | 19 | 13 |
Minimum | 65 | 69 |
Maximum | 84 | 82 |
Sum | 4579 | 4601 |
Count | 61 | 61 |
Analysis of descriptive statistics shows that both the current and the proposed plan have almost similar mean completion hours which stand at 75.06 and 75.42 for the current and proposed respectively. Both the plans have exact same median and mode. However, the standard deviation in the current plan (3.94) is higher than that in the proposed plan (2.56), which is ultimately leading to the higher variance in the current plan. This suggests that the completion hours are more dispersed the mean value in the current plan, hence the mean does not give the true picture of data distribution whereas in the proposed plan, data for completion hours is comparatively more...

...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 something happens. As I examined on what the statement says, the phrase “number of times something happens” really caught my attention because my subconscious says “here we go again the non-stop solving, analyzing of problems” and I was right. This course of basic statistic has provided me with the analytical skills to crunch numerical data and to make inference from it. At first I thought that I will be alright all along with this subject but it seems that just some part of it maybe it is because I don’t pay much of my attention to it but I have learned many things. I have learned my lesson.
During our every session in this subject before having our midterm examination I really had hard and bad times in coping up with this subject. When we have our very first quiz I thought that I would fail it but it did not happen but after that, my next quizzes I have taken I failed. I was always feeling down when in every quiz I failed because even though I don’t like this...

...2a) a) Increasing the difference between 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 bring the samples mean closer to the population mean so z score will get smaller.
4a) The boundaries for critical region, when alpha level is is changed from α = .05 to .01, the size of the critical region will increase in size and the boundaries will be closer to the center of the distribution. This will allow me to see if there is error or not and also accept or reject the null hypothesis. If the alpha level is changed from .05 to .01
a) what happens to the boundaries for the critical region?
It reduces the power of the test to prove the hypothesis.
You increase the chance of rejecting a true H
b) what happens to the probability of a type 1 error?
Type 1 error is falsely reporting a hypothesis,
Where you increase the chance that you will reject a true null hypothesis.
4b) The probability of a Type I error is determined by the alpha level. Since the alpha level has decreased, we can expect increase in...

...
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 location are are related. Use α = 0.05. Explain your results.
Pearson Chi-Square = 37.159, DF = 3, P-Value = 0.000
Likelihood Ratio Chi-Square = 40.039, DF = 3, P-Value = 0.000
The P value associated with out chi square is 0.00 and the Alpha level is 0.05 so we reject the null hypothesis. The P- value is less than the alpha level. So, we conclude that style of homes and locations are not related.
[10 pts] 2. Use the data set TEMCO.MTW in the Student14 folder. Perform the Chi
Square test for independence to determine whether department and gender are related. Use α = 0.05. Explain your results.
Pearson Chi-Square = 1.005, DF = 3, P-Value = 0.800
Likelihood Ratio Chi-Square = 1.012, DF = 3, P-Value = 0.798
The P-value associated with out chi square is 0.800 and the Alpha level is 0.05 we can see that we are unable to reject the null hypothesis. The P- value is greater than the alpha level. So, we conclude that departments and gender are related..
[30 pts] 3. Use the data set...

...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 businessstatistics is too much work because it entails a detailed decision making process that includes calculations, I feel that without educating yourself on the processes first you wouldn’t know how to imply statistics. This is a tool managers will need in order to run a successful business. In this paper I will review types of statistical elements like: Descriptive, Inferential, hypothesis development and testing and the evaluation of the results. Also I will discuss what I have learned from business statistics.
My description of Descriptive statistics is that they are the numerical elements that make up a data that can refer to an amount of a categorized description of an item such as the percentage that asks the question, “How many or how much does it take to “ and the outcome numerical amount. According to “Dr. Ashram’s Statistics site” “The quantities most commonly used to measure the dispersion of the values about...

...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 trials with the current and 40 trials with the new golf balls. The testing was performed with a mechanical fitting machine so that any difference between the mean distances for the two models could be attributed to a difference in the design. The outcomes are given in the table of appendix 1.
3. Hypothesis testing
The first thing to do is to formulate and present the rationale for a hypothesis test that Par, Inc. could use to compare the driving distance of the current and new golf balls. By formulation of these hypothesis there is assumed that the new and current golf balls show no significant difference to each other. The hypothesis and alternative hypothesis are formulated as follow:
Question 1
H0 : µ1 - µ2 = 0 (they are the same)
Ha : µ1 - µ2 ≠ 0 (the are not the same)
4. P-value
Secondly; analyze the data to provide the hypothesis testing conclusion. The p-value for the test is:
Question 2
Note: the statistical data is provide in § 5.
-one...

...Organization of Terms
Experimental Design
Descriptive
Inferential
Population
Parameter
Sample
Random
Bias
Statistic
Types of
Variables
Graphs
Measurement scales
Nominal
Ordinal
Interval
Ratio
Qualitative
Quantitative
Independent
Dependent
Bar Graph
Histogram
Box plot
Scatterplot
Measures of
Center
Spread
Shape
Mean
Median
Mode
Range
Variance
Standard deviation
Skewness
Kurtosis
Tests of
Association
Inference
Correlation
Regression
Slope
y-intercept
Central Limit Theorem
Chi-Square
t-test
Independent samples
Correlated samples
Analysis-of-Variance
Glossary of Terms
Statistics - a set of concepts, rules, and procedures that help us to:
organize numerical information in the form of tables, graphs, and charts;
understand statistical techniques underlying decisions that affect our lives and well-being; and
make informed decisions.
Data - facts, observations, and information that come from investigations.
Measurement data sometimes called quantitative data -- the result of using some instrument to measure something (e.g., test score, weight);
Categorical data also referred to as frequency or qualitative data. Things are grouped according to some common property(ies) and the number of members of the group are recorded (e.g., males/females, vehicle type).
Variable - property of an object or event that can take on different values. For example,...

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