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What is the sampling distribution of p hat?

The sampling distribution of (\hat{p}) (the sample proportion) describes the distribution of sample proportions obtained from repeated random samples of a given size from a population. It is approximately normal when the sample size is large enough, typically when both (np) and (n(1-p)) are greater than 5, where (p) is the population proportion and (n) is the sample size. The mean of this distribution is equal to the population proportion (p), and the standard deviation (standard error) is given by (\sqrt{\frac{p(1-p)}{n}}).


What is sample distribution of the sample proportion?

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.


What proportion of a normal distribution corresponds to z-scores greater than plus 1.04?

To find the proportion of a normal distribution corresponding to z-scores greater than +1.04, you can use the standard normal distribution table or a calculator. The area to the left of z = 1.04 is approximately 0.8508. Therefore, the proportion of the distribution that corresponds to z-scores greater than +1.04 is 1 - 0.8508, which is approximately 0.1492, or 14.92%.


Why is the normal distribution appropriate when comparing the proportions of defective of 2 populations with a sample size greater than 30 and p close to 5 for both populations?

It provides a good approximation to the binomial distribution when np and n(1-p) are greater than 5 for each population.


What proportion of a normal distribution corresponds to z scores greater than 1.04?

In a normal distribution, approximately 76.4% of the data falls below a z score of 1.04. Therefore, the proportion of the distribution that corresponds to z scores greater than 1.04 is about 23.6%. This can be found using standard normal distribution tables or calculators.


What is the proportion of observations from a standard Normal distribution that take values greater than 0.84?

In a standard normal distribution, approximately 20.4% of the observations are greater than 0.84. This can be determined using the cumulative distribution function (CDF) for the standard normal distribution, which shows that about 79.6% of values fall below 0.84. Therefore, the proportion greater than 0.84 is 1 - 0.796 = 0.204, or 20.4%.


According to a study conducted in one city 36 of adults have credit card debts more than $2000. A simple random sample of n 200 adults is obtained from the city. Describe the sampling distribution?

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.


A normal distribution has a mean of µ = 50 with σ = 10. What proportion of the scores in this distribution are greater than X = 65?

Scores on the SAT form a normal distribution with a mean of µ = 500 with σ = 100. What is the probability that a randomly selected college applicant will have a score greater than 640? ​


Which statement is true about the population proportion of defective pieces in the 2000 items?

The statement that the proportion of defective pieces is not less than 0 nor greater than 1.


Can the slope of a lorenz curve be greater than 1?

No, the slope of a Lorenz curve cannot be greater than 1. The Lorenz curve represents the cumulative distribution of income or wealth, and its slope reflects the proportion of total income earned by a certain percentage of the population. Since the curve plots cumulative shares of income against cumulative shares of the population, the maximum slope occurs at the point where the entire population earns all the income, which results in a slope of 1.


In a hypothesis for a proportion when may normality be assumed?

If n*p is greater than or equal to 5 AND n*q is greater than or equal to 5, you can use a normal distribution as an estimate for the binomial distribution. Recall, n is the number of trials, p is the probability of success of a trial, and q is 1-p.


What is index all about?

The Swaroopâ??s index is the proportion of deaths of people aged 50 years and up. The higher the Swaroopâ??s index of a population, the greater the proportion of the deaths who were able to reach the age of 50 years.