Constructing Confidence Intervals In Exercises 35–38, you are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. 36. Stock Prices From a random sample of 36 business days from February 24, 2016, through February 24, 2017, the mean closing price of Apple stock was $116.16. Assume the population standard deviation is $10.27. (Source: Nasdaq)
Constructing Confidence Intervals In Exercises 35–38, you are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.
36. Stock Prices From a random sample of 36 business days from February 24, 2016, through February 24, 2017, the mean closing price of Apple stock was $116.16. Assume the population standard deviation is $10.27. (Source: Nasdaq)
Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.
A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
A Problem Solving Approach To Mathematics For Elementary School Teachers (13th Edition)
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Hypothesis Testing and Confidence Intervals (FRM Part 1 – Book 2 – Chapter 5); Author: Analystprep;https://www.youtube.com/watch?v=vth3yZIUlGQ;License: Standard YouTube License, CC-BY