The confidence interval for population mean: ? is known (10 points) Administrators at a diamond drilling company want to know how much money they spent on equipment for the holes that were drilled in the past year. Of the holes drilled in the past year, a random sample of 200 holes was selected. The sample mean for money spent per hole drilled was $5,230. The administrators want to develop a 90% confidence interval estimate. Past studies have shown that the population standard deviation is σ = $500. (The sampling distribution is normally distributed and the critical value will be a z-value from the standard normal distribution) (a) Determine the standard error of the sampling distribution. (b) Determine the critical value, z, from the standard normal table. (c) Compute the confidence interval estimate for 90% confidence interval. (d) Compute the confidence interval estimate for 95% confidence interval.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
The confidence interval for population mean: ? is known (10 points) Administrators at a diamond drilling company want to know how much money they spent on equipment for the holes that were drilled in the past year. Of the holes drilled in the past year, a random sample of 200 holes was selected. The sample mean for money spent per hole drilled was $5,230. The administrators want to develop a 90% confidence
(a) Determine the standard error of the sampling distribution.
(b) Determine the critical value, z, from the standard normal table.
(c) Compute the confidence interval estimate for 90% confidence interval. (d) Compute the confidence interval estimate for 95% confidence interval.
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