A 95% confidence interval implies that Group of answer choices with repeated sampling, 95% of the intervals constructed would contain the parameter of interest. There is a 95% probability of capturing the parameter of interest within our interval. 95% of the data lies with our interval. None of the above. In reality, the factor(s) to be considered when assessing if the Central Limit Theorem holds is/are Group of answer choices the shape of the distributions of the original variable. The sample size. Both of the above. None of the above; we only need n≥30n≥30. Select all that apply. The z-distribution Group of answer choices has a mean of zero. Is a normal distribution. Has a standard deviation of 1. Has an infinite number of distributions.

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A 95% confidence interval implies that  Group of answer choices with repeated sampling, 95% of the intervals constructed would contain the parameter of interest. There is a 95% probability of capturing the parameter of interest within our interval. 95% of the data lies with our interval. None of the above.  In reality, the factor(s) to be considered when assessing if the Central Limit Theorem holds is/are  Group of answer choices the shape of the distributions of the original variable. The sample size. Both of the above. None of the above; we only need n≥30n≥30.  Select all that apply.  The z-distribution  Group of answer choices has a mean of zero. Is a normal distribution. Has a standard deviation of 1. Has an infinite number of distributions.

Lacey-May Snyder · Accepted Answer

Step 1  A 95% confidence for population parameter signifies that there is 95% confidence or it can be said as there is 95% surety that the population parameter will lie in that interval.  The central limit theorem states that as the sample size increases, the sampling distribution more closely approximates the normal distribution.  Conventionally, z is used to represent the random variable which follows standard normal distribution.        Step 2  (1).  If a sample is taken from a population randomly and on the basis of analysis of that sample, the 95% confidence interval for population parameter is estimated. And this process is repeated several times, then it can be observed that out of all estimated confidence intervals for population parameter, 95% of them will contain the actual value of population parameter.  Hence, the option which states &quot;with repeated sampling, 95% of the intervals constructed would contain the parameter of interest&quot; is correct.  Step 3  (2).  The central limit theorem states that as the sample size increases, the sampling distribution more closely approximates the normal distribution and further if the sample size is greater than or equal to 30 then, the sample can be considered as large enough to approximate its distribution by normal distribution, irrespective of any other parameter.  Hence, the option which states &quot;none of the above; we only need n≥30&quot; is correct.  Step 4  (3).  A normal distribution is termed as standard normal distribution if the mean value of random variable is 0 and standard deviation associated with random variable is 1.  z denotes standard normal random variable. This implies that z-distribution is normal distribution with 0 mean value and standard deviation of 1.   Hence, the first three options are correct.

A 95% confidence interval implies that Group of answer choices with repeated

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