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ADMS 2320 Study Guide - Test Statistic, Type I And Type Ii Errors, Null Hypothesis

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School
York University
Department
Administrative Studies
Course
ADMS 2320
Professor
Elena Skliarenko

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Document Summary

: value of z such that the area to its right is equal to. Confidence interval estimator of with known (+ or -, so it"s 2 tail : . Wilson estimator t-test of : t-estimator of : . Estimate the mean to within w units: . Confidence interval estimator of using the wilson estimator. : the area in the lower tail or upper tail of the sampling distribution of the sample mean. Confidence interval estimator of the total of a large finite population. Type i error: reject a true null hypothesis; probability: (significant level) Type ii error: not reject a false null hypothesis. Confidence interval estimator of the total number of success in a large finite population. If less than rejection region, cannot reject the null hypothesis in favor of the alternative. When is known, to test a population mean.

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Related Questions

1. A sample size of n=15 is a simple random sample selected from a normally distributed population. Using Table C, find the critical value t* corresponding to a 95% confidence level in the following scenarios:

a.............to construct a confidence interval 

b..............one-sided hypothesis test 

c..............two-sided hypothesis test

 

 

The reading on a voltage meter connected to a test circuit is uniformly distributed over the interval (θ, θ+1), where θ is the true but unknown voltage of the circuit. Suppose that Y1, Y2,..... Yn denotes a random sample of such readings.

a. Show that Y(bar) is a biased estimator of θ and compute the bias.

b. Find a function of Y(bar) that is an unbiased estimator of θ.

 

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample mean, x¯\bar{x}ˉ, is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9. (a) Construct the 90% confidence interval for the population mean if the sample size, n, is 15. (b) Construct the 90% confidence interval for the population mean if the sample size, n, is 25. How does increasing the sample size affect the width of the interval? (c) Construct the 95% confidence interval for the population mean if the sample size, n, is 15. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the confidence interval? (d) Construct the 90% confidence interval for the population standard deviation if the sample size, n, is 15.