A company has a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these gems is x ¯ = 6.75 carats, and the sample standard deviation is s = 0.33 carat. Let μ be the mean weight for the distribution of all sapphires produced by the new process. ( Show your work, no work shown, no credit given) What is degrees of freedom in this problem Use table or Technology to find t-critical value with degrees of freedom found in above and with α = 0.05significance level. Find the Margin of error (E) Find 95% confidence interval for μ Interpret the confidence interval in the context of the problem.
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.
A company has a new process for manufacturing large artificial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these gems is x ¯ = 6.75 carats, and the sample standard deviation is s = 0.33 carat. Let μ be the mean weight for the distribution of all sapphires produced by the new process. ( Show your work, no work shown, no credit given)
- What is degrees of freedom in this problem
- Use table or Technology to find t-critical value with degrees of freedom found in above and with α = 0.05significance level.
- Find the Margin of error (E)
- Find 95% confidence interval for μ
- Interpret the confidence interval in the context of the problem.
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