The sample distribution of the sample proportion refers to the probability distribution of the proportion of successes in a sample drawn from a population. It is typically approximated by a normal distribution when certain conditions are met, specifically when the sample size is large enough (usually np and n(1-p) both greater than 5). The mean of this distribution is equal to the population proportion (p), and the standard deviation is calculated using the formula √[p(1-p)/n]. This distribution is useful for making inferences about the population proportion based on sample data.
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The sampling distribution of the sample proportion of adults with credit card debts greater than $2000 can be described using the population proportion, which is 36% (or 0.36). For a simple random sample of 200 adults, the mean of the sampling distribution will be equal to the population proportion (0.36), and the standard error can be calculated using the formula ( \sqrt{\frac{p(1-p)}{n}} ), where ( p ) is the population proportion and ( n ) is the sample size. In this case, the standard error would be approximately ( \sqrt{\frac{0.36(0.64)}{200}} ), leading to a normal distribution centered at 0.36, assuming the sample size is sufficiently large.
for a normal-shaped distribution with n=50 and siqma =8 : a- what proportion of the scores have values between 46 and 54? b- for samples of n= 4, what means have values what proportion of the sample mean have values between 46 and 54? c- for samples of n= 16, what means have values what proportion of the sample mean have values between 46 and 54?
No, the sample mean and sample proportion are not called population parameters; they are referred to as sample statistics. Population parameters are fixed values that describe a characteristic of the entire population, such as the population mean or population proportion. Sample statistics are estimates derived from a sample and are used to infer about the corresponding population parameters.
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The sampling distribution of the sample proportion of adults with credit card debts greater than $2000 can be described using the population proportion, which is 36% (or 0.36). For a simple random sample of 200 adults, the mean of the sampling distribution will be equal to the population proportion (0.36), and the standard error can be calculated using the formula ( \sqrt{\frac{p(1-p)}{n}} ), where ( p ) is the population proportion and ( n ) is the sample size. In this case, the standard error would be approximately ( \sqrt{\frac{0.36(0.64)}{200}} ), leading to a normal distribution centered at 0.36, assuming the sample size is sufficiently large.
i THINK IT IS .05
I dont really konw im doing this for the pnits srry
for a normal-shaped distribution with n=50 and siqma =8 : a- what proportion of the scores have values between 46 and 54? b- for samples of n= 4, what means have values what proportion of the sample mean have values between 46 and 54? c- for samples of n= 16, what means have values what proportion of the sample mean have values between 46 and 54?
The distribution of the sample mean is bell-shaped or is a normal distribution.
The distribution of sample means will not be normal if the number of samples does not reach 30.
No, the sample mean and sample proportion are not called population parameters; they are referred to as sample statistics. Population parameters are fixed values that describe a characteristic of the entire population, such as the population mean or population proportion. Sample statistics are estimates derived from a sample and are used to infer about the corresponding population parameters.
The sampling proportion may be used to scale up the results from a sample to that of the population. It is also used for designing stratified sampling.