Module 13: Sample Size Determination and Intro to Hypothesis Testing This module is divided into 2 distinct parts: I. Sample Size Determination when estimating: A. The Population Mean ( ) B. The Population Proportion (P) Note: When ever calculating samples sizes, ALWAYS round up to the next whole number. You can't, for example, sample .25 of a person. II. Introduction to Hypothesis testing The first part is fairly straightforward and just a matter of applying a formula based on desired criteria. Hypothesis testing is more involved and involves strict adherence to an eight-step process.
Module 13: Sample Size Determination and Intro to Hypothesis Testing I. Sample Size Determination A. The Population Mean ( ) When estimating , the sample size is determined using the following formula: n = Where: Based on the level of confidence exactly as in Modules 11 and 12 (see next slide to refresh your memory) = The standard deviation. If unknown, = 1/4 the range. E = The amount of error we're willing to live with. The smaller the error, the larger the sample size required. As a statistician, however, the larger the sample size, the more costly the study. Therefore it's a tradeoff. We know larger sample sizes increase accuracy and reduce error, but is the reduction in error worth the increase in cost? This, of course, is a subjective question. •
Module 13: Sample Size Determination and Intro to Hypothesis Testing I. Sample Size Determination Factors for various confidence levels: • Confidence α α/2 Z α/2 Z α/2 0.99 0.01 0.005 Z .005 2.5758 =NORMSINV(0.005)*-1 0.98 0.02 0.01 Z .01 2.3263 =NORMSINV(0.01)*-1 0.96 0.04 0.02 Z .02 2.0537 =NORMSINV(0.02)*-1 0.95 0.05 0.025 Z .025 1.9600 =NORMSINV(0.025)*-1 0.90 0.10 0.05 Z .05 1.6449 =NORMSINV(0.05)*-1 0.85 0.15 0.075 Z .075 1.4395 =NORMSINV(0.075)*-1 0.80 0.20 0.10 Z .10 1.2816 =NORMSINV(0.1)*-1
Module 13: Sample Size Determination and Intro to Hypothesis Testing I. Sample Size Determination Example 1 : A researcher wants to estimate the average monthly expenditure om bread by a family in Chicago. She wants to be 90% confident of her results and wants to be within $1.00 of the actual figure. The standard deviation of monthly bread purchases in Chicago is known to be $4.00. How large a sample size should she take? From the table on slide 3, we know that = 1.6449since she desires a 90% level of confidence. From the text of the question we know = 4 From the text of the question, we also know E = 1. E = 1 since she wants to be within $1 of the actual number. That is, in effect, the amount of error she's willing to live with. Plugging this information into our formula yields: n == = = 43.2911. Therefore n = 44* * Again, with sample size, we always round up to the next whole number. •
Module 13: Sample Size Determination and Intro to Hypothesis Testing I. Sample Size Determination Example 2: Suppose you want to estimate the average age of all Boeing 727s currently in active domestic service in the U.S. You want to be 95% confident of your results and want the estimate to be within 2 years of the actual age. The first Boeing 727 was placed in active service 40 years ago, but none of the planes in the U.S. domestic fleet are older than 25 years. How large a sample size should you take?
- Spring '14
- Null hypothesis, Statistical hypothesis testing