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In a sample of 500 students 50 percent attend college within 50km of their homes The probability that the population proportion will be between 0.45 and 0.55 is?
Wiki User
∙ 14y ago
According to the theory behind a sampling distribution of a proportion, when you take a sample proportion with mean p from a sample of n people, the actual population proportion will follow a normal distribution of mean p with a standard deviation of √(p*(1-p)/n). Using the information given, our sample had a mean, p, of .5 and a sample size, n, of 500. Therefore, the mean of the population is .5 and the standard deviation is √(.5*(1-.5)/500)=.022361.
Next, in order to find our probability, we need to calculate the z-scores of our 2 bounds using the formula z=(x-mean)/standard deviation. For .45 this gives (.45-.5)/.022361=-2.236 and for .55 we get (.55-.5)/.022361=2.236. In order to convert this into a probability, we will need to look these values up in a z-table and find the area between them. Doing that we find that the area must be .974653. This tells us that the probability that the population proportion is between 0.45 and 0.55 is 97.4653%.
Wiki User
∙ 14y ago
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What are the differences between probability sampling and non probability sampling?
In a probability sample, each unit has the same probability of being included in the sample. Equivalently, given a sample size, each sample of that size from the population has the same probability of being selected. This is not true for non-probability sampling.
What is the difference between experimental and theoretical probability?
The difference between experimental probability and theoretical probability is that experimental probability is the probability determined in practice. Theoretical probability is the probability that should happen. For example, the theoretical probability of getting any single number on a number cube is one sixth. But maybe you roll it twice and get a four both times. That would be an example of experimental probability.
What is the difference between probability and actuality?
probability is a guess and actuality is what will happen
What is the relationship between the probability of a simple event and its complement?
If the probability of an event is p, then the complementary probability is 1-p.
Is -0.0031 probability?
No, a probability is a number between 0 (included) and 1 (included)
What is difference between proportion and probability?
Proportion is the probability of a selected sample. probability is the true probability of all cases. If this is not what you are looking for then please specify.
Range of values for proportion and probability?
A proportion is usually between 0 and 1. A probability is always between 0 and 1, inclusive; 0 being impossible and 1 being certain.
What is the difference between 'probability' and 'proportion'?
well a proportion compares part of a quanity to the whole quanity called the base using a percentprobabiltyis the cahnce of an event happening for example like getting a puppy that is a simple event
If 68 percent of IQ scores are between 85 and 115 what is the probability of meeting a person in the population within that IQ range?
The probability is 0.68
What are the differences between probability sampling and non probability sampling?
In a probability sample, each unit has the same probability of being included in the sample. Equivalently, given a sample size, each sample of that size from the population has the same probability of being selected. This is not true for non-probability sampling.
What is a statement of equality between two ratios called?
... a proportion.... a proportion.... a proportion.... a proportion.
Can -0.32 be a probability?
No, -0.32 can not be a probability. Probability ranges between 0 and 1.
Proportion between 16 and 4?
It is: 4 to 1
How do you solve the proportion of something?
There cannot be a "proportion of something": proportion is a relationship between two things, and how you solve it depends on whether they (or their transformations) are in direct proportion or inverse proportion.
What is sequence in probability?
There is no relationship between sequences and probability.
Can the number 352 form a proportion?
No, no number by itself can form a proportion. A proportion is a relationship between two numbers.
If 135 out of 500 students sampled have computers what is the 95-percent confidence interval for the true proportion of all students who own computers?
First identify the proper confidence interval. Since we are dealing with one proportion, a 1-proportion Z-interval is appropriate. Now check to see if the necessary conditions are fulfilled. First is whether the data was collected from a simple random sample representative of the population. Second is whether n * p-hat and n * (1 - p-hat) are both sufficiently large, where n is the sample size and p-hat is the sample proportion. This is the case, since both 135 and 500 - 135 = 365 are both greater than 10, a generally accepted value. Third is whether n is a sufficiently small fraction of the population (about 1/10 of the population is the largest acceptable fraction). If you have at least 5000 students in your population, the test can be used. Finally, the calculation (assuming all conditions have been fulfilled). The confidence interval for a proportion is p-hat +/- z-star * sqrt(p-hat * (1 - p-hat) / n). Here z-star is the critical value for which P(abs(Z) > z-star) on the standard normal curve is equal to 1 minus your confidence level. In this case, we're looking for the value where the probability of a standard normal random variable producing a value either greater than z-star or less than negative z-star is 1 - .95 = 0.05. This value is approximately 1.96. Putting it all together: p-hat = 135/500 = 0.27z-star = 1.96n = 5000.27 +/- 1.96 * sqrt(0.27 * 0.73 / 500)0.27 +/- 1.96 * sqrt(0.0003942)0.27 +/- 1.96 * .01990.27 +/- .03891We are 95% confident that the true proportion of students who own computers is between .23109 and .30891.
