FORESTRY
AGRICULTURAL STATISTICS AND ECONOMICS
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Question
[CLICK ON ANY CHOICE TO KNOW THE RIGHT ANSWER]
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z can be used only for large samples
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z requires that you know the population standard deviation
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z requires that you can regard your data as an SRS from the population
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z requires that the sample size is at most 10% of the population size
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a z critical value will lead to a wider interval than a t critical value
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Detailed explanation-1: -Question: One reason for a t distribution instead of the normal curve to find critical values when calculating a level C confidence interval for a population mean is that the standard normal table doesn’t include confidence levels at the bottom. a z critical value will lead to a wider interval than a t critical value.
Detailed explanation-2: -When we use “t” instead of “Z” in the equation for the confidence interval, it will result in a larger margin of error and a wider confidence interval reflecting the smaller sample size.
Detailed explanation-3: -When we know the population standard deviation , we use a standard normal distribution to calculate the error bound EBM and construct the confidence interval. We need to find the value of z that puts an area equal to the confidence level (in decimal form) in the middle of the standard normal distribution Z N(0, 1).
Detailed explanation-4: -The t-distribution is used as an alternative to the normal distribution when sample sizes are small in order to estimate confidence or determine critical values that an observation is a given distance from the mean.