How to Determine Sample Size, Determining Sample Size?

In order to prove that a process has been improved, you must measure the process capability before and after improvements are implemented. This allows you to quantify the process improvement (e.g., defect reduction or productivity increase) and translate the effects into an estimated financial result – something business leaders can understand and appreciate. If data is not readily available for the process, how many members of the population should be selected to ensure that the population is properly represented? If data has been collected, how do you determine if you have enough data?

 

Determining sample size is a very important issue because samples that are too large may waste time, resources and money, while samples that are too small may lead to inaccurate results. In many cases, we can easily determine the minimum sample size needed to estimate a process parameter, such as the population mean  .

 

When sample data is collected and the sample mean   is calculated, that sample mean is typically different from the population mean . This difference between the sample and population means can be thought of as an error. The margin of error  is the maximum difference between the observed sample mean  and the true value of the population mean   :

 

 

where|

 is known as the critical value, the positive  value that is at the vertical boundary for the area of  in the right tail of the standard normal distribution.

  

 is the population standard deviation.

 

  is the sample size.

 

 

Rearranging this formula, we can solve for the sample size necessary to produce results accurate to a specified confidence and margin of error.

 

This formula can be used when you know  and want to determine the sample size necessary to establish, with a confidence of  , the mean value    to within . You can still use this formula if you don’t know your population standard deviation  and you have a small sample size. Although it’s unlikely that you know   when the population mean is not known, you may be able to determine  from a similar process or from a pilot test/simulation.

Let’s put all this statistical mumbo-jumbo to work. Take for example that we would like to start an Internet service provider (ISP) and need to estimate the average Internet usage of households in one week for our business plan and model.

 

Sample Size Calculation Example

 

Problem

We would like to start an ISP and need to estimate the average Internet usage of households in one week for our business plan and model. How many households must we randomly select to be 95 percent sure that the sample mean is within 1 minute of the population mean . Assume that a previous survey of household usage has shown  = 6.95 minutes.

 

Solution

We are solving for the sample size 

  .

 

A 95% degree confidence corresponds to  = 0.05. Each of the shaded tails in the following figure has an area of     = 0.025. The region to the left of     and to the right of    = 0 is 0.5 – 0.025, or 0.475. In the table of the standard normal () distribution, an area of 0.475 corresponds to a  value of 1.96. The critical value is therefore    = 1.96.

 

 The margin of error  = 1 and the standard deviation   = 6.95. Using the formula for sample size, we can calculate :

 

So we will need to sample at least 186 (rounded up) randomly selected households. With this sample we will be 95 percent confident that the sample mean   will be within 1 minute of the true population of Internet usage.

 

This formula can be used when you know  and want to determine the sample size necessary to establish, with a confidence of  , the mean value   to within  . You can still use this formula if you don’t know your population standard deviation  and you have a small sample size. Although it is unlikely that you know  when the population mean is not known, you may be able to determine  from a similar process or from a pilot test/simulation.

Defining Narco-Terrorism

The challenges posed by drug trafficking, organized crime and terrorism are so complex that attempts to simplify them are understandable. In order to gain public support for increased investment in law enforcement, a military and police intervention, or an increase in taxes for instance, policy officials often attempt to describe intricate problems in simplistic terms. This, notably coupled with the media’s inclination for sensationalist stories, academics’ search for government funding, and the immediate overreaction that ‘terrorism’ provokes, has contributed to the emergence of the term ‘narco-terrorism’ and related policies and analysis amalgamating terrorism and the drug trade.

However, this approach often has negative – albeit often unintended – consequences, including: skewing policy priorities and neglecting related issues such as arms trafficking, human trafficking, cigarette smuggling, corruption, state abuses as the focus remains on terrorism, drug trafficking and the links in between; ignoring local specificities by drawing on the widely-held assumption of an automatic relationship between any terrorist and drug trafficker; underestimating the differences in motives and interests between terrorist organizations and drug traffickers (e.g. very often, the former look for attention while the latter evade it), thus misjudging their potential responses to policy and law enforcement changes; putting in place misguided heavy-handed policies to respond to problems that are intrinsically political, economic and social; and ultimately creating a disproportionate sense of fear and causing political overreaction, thereby playing into the hands of terrorists, with potential counterproductive effects. Crucially, drug trafficking and other types of illicit trade and organized crime are important issues in their own right, and should not need the ‘terrorism’ label to attract attention.

Given the persistence of international challenges related to drug trafficking, other types of illicit trade, organized crime, corruption, weak governance, and terrorism, developing a more nuanced understanding of the problems at stake would go a long way in addressing them more appropriately. The narratives and policies of the War on Drugs and War on Terror are increasingly recognized as inadequate, but much remains to be done towards a more balanced, comprehensive, and effective set of policies. No longer conflating terrorism and drug trafficking would be a first step in the right direction.

10 HEALTH BENEFITS OF SEX

1 . Having sex relieves headaches. Every time you make love, it releases the tension in the veins of the brain.

2. A lot of sex can clear the stuffy nose. Sex is a natural antihistamine. It helps to fight against asthma and spring allergies.

3. Making love is a spectacular beauty treatment. Scientists have discovered that when a woman has sex, it produces a large amount of estrogen that gives shine and softness to hair.

4. Sex is one of the safest sports. Make love often strengthens the muscles of male and female body. It’s more enjoyable than swimming 20 laps in the pool and there is no need special shoe!

5. Make love slowly, smoothly and in a relaxed way reduces the chances of suffering dermatitis, skin rashes and acne. The sweat produced cleanses the pores and makes your skin glow.

6. Lovemaking can burn all the calories you have accumulated during the romantic dinner before bedtime.

7. Sex is a divine remedy for depression. It releases endorphins into the bloodstream, creating a state of euphoria and leaving women and men with the feeling of being unique.10 health benefits of sex you need to know

8. Sex is the tranquilizer and muscle relaxant to a safer world. It is a thousand times more effective than Valium.

9. Sexually active body releases more pheromones. .

10. Kissing each day will keep you more time away from the dentist. Kissing is an art which makes the cleaner teeth and saliva reduces the amount of acid that causes tooth decay. This prevention eliminates many problems, in addition to offering a breath constantly renewed!

15 SPECTACULAR TRICKS FOR YOUR BODY !!!!

1.) If you've got an itch in your throat, scratch your ear. When the nerves in the ear get stimulated, they create a reflex in the throat that causes a muscle spasm, which cures the itch. 

2.) Having trouble hearing someone at a party or on the phone? Use your right ear it's better at picking up rapid speech. But, the left is better at picking up music tones.

3.) If you need to relieve yourself BADLY, but you're not anywhere near a bathroom, fantasize about RELATIONS. That preoccupies your brain and distracts it.

4.) Next time the doctor's going to give you an injection, COUGH as the needle is going in. The cough raises the level of pressure in your spinal canal, which limits the pain sensation as it tries to travel to your brain.

5.) Clear a stuffed nose or relieve sinus pressure by pushing your tongue against the roof of your mouth then pressing a finger between your eyebrows. Repeat that for 20 seconds it causes the vomer bone to rock, which loosens your congestion and clears you up.

6.) If you ate a big meal and you're feeling full as you go to sleep,lay on your left side. That will keep you from suffering from acid reflux it keeps your stomach lower than your esophagus, which will helps keep stomach acid from sliding up your throat.

7.) You can stop a toothache by rubbing ice on the back of your hand, on the webbed area between your thumb and index finger. The nerve pathways there stimulate a part of the brain that blocks pain signals from your mouth.

8.) If you get all messed up on liquor, and the room starts spinning, put your hand on something stable. The reason: Alcohol dilutes the blood in the part of your ear called the cupula, which regulates balance. Putting your hand on something stable gives your brain another reference point, which will help make the world stop spinning.

9.) Stop a nose bleed by putting some cotton on your upper gums right behind the small dent below your nose and press against it hard. Most of the bleeding comes from the cartilage wall that divides the nose, so pressing there helps get it to stop.

10.) Nervous? Slow your heart rate down by blowing on your thumb. The vagus nerve controls your heart rate, and you can calm it down by breathing.

11.) Need to breathe underwater for a while? Instead of taking a huge breath, HYPERVENTILATE before you go under, by taking a bunch of short breaths. That will trick your brain into thinking it has more oxygen, and buy you about 10 extra seconds.

12.) You can prevent BRAIN FREEZE by pressing your tongue flat against the roof of your mouth, covering as much surface area as possible. Brain freeze happens because the nerves in the roof of your mouth get extremely cold, so your brain thinks your whole body is cold. It compensates by overheating which causes your head to hurt. By warming up the roof of your mouth, you'll chill your brain and feel better.

13.) If your hand falls asleep, rock your head from side to side. That will wake your hand or arm up in less than a minute. Your hand falls asleep because of the nerves in your neck compressing so loosening your neck is the cure. If your foot falls asleep, that's governed by nerves lower in the body, so you need to stand up and walk around.

14.) Finally, this one's totally USELESS, but a nice trick. Have someone stick their arm out to the side, straight, palm down. Press down on his wrist with two fingers. He'll resist, and his arm will stay horizontal. Then, have him put his foot on a surface that's half an inch off the ground, like a stack of magazines, and do the trick again. Because his spine position is thrown off, his arm will fall right to his side, no matter how much he tries to resist.

15.) Got the hiccups? Press thumb and second finger over your eyebrows until the hiccups are over - usually, in a short while.