Section 4 Module 14 Power Point (Hypothesis Testing for Single Populations Part 1)(1) - Module 14 Hypothesis Testing for Single Populations Part 1 This

# Section 4 Module 14 Power Point (Hypothesis Testing for Single Populations Part 1)(1)

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Module 14: Hypothesis Testing for Single Populations Part 1This module is divided into 2 parts:I.Hypothesis Testing for a Single Population Mean, Large Sample Size (n 30)II. Hypothesis Testing for a Single Population Mean, Small Sample Size (n < 30)This is not fundamentally different from what we were doing in Module 13, but now we’ll add some complexity, including the Finite Correction Factor FCF).
Module 14: Hypothesis Testing for Single Populations Part 1Z Factor for 2-Tail TestsZ Factor for 1-Tail Testsαα/2Zα/2Zα/2αZα0.010.005Z.0052.5758=NORMSINV(0.005)*-10.01Z.012.3263=NORMSINV(0.01)*-10.020.01Z.012.3263=NORMSINV(0.01)*-10.02Z.022.0537=NORMSINV(0.02)*-10.040.02Z.022.0537=NORMSINV(0.02)*-10.04Z.041.7507=NORMSINV(0.04)*-10.050.025Z.0251.9600=NORMSINV(0.025)*-10.05Z.051.6449=NORMSINV(0.05)*-10.100.05Z.051.6449=NORMSINV(0.05)*-10.10Z.051.2816=NORMSINV(0.1)*-10.150.075Z.0751.4395=NORMSINV(0.075)*-10.15Z.151.0364=NORMSINV(0.15)*-10.200.10Z.101.2816=NORMSINV(0.1)*-10.20Z.200.8416=NORMSINV(0.2)*-1
Module 14: Hypothesis Testing for Single Populations Part 1I.Hypothesis Testing for a Single Population Mean, Large Sample Size (n 30)Example 1:A nationwide survey of CPAs found that the average net income for sole practitioner CPAs was \$74,914. A believes this figure does not apply to sole practitioner CPAs in the state of South Dakota. The researcher takes a random sample of 112 sole practitioner CPAs in South Dakota which results in a sample mean net income of \$78, 695 with a sample standard deviation of \$14,530. At the .05 level of significance, test to determine if the mean net income of sole practitioner CPAs in South Dakota is different from the national average. Step 1: Note: In this test, we want to determine if the net income is different. We are not trying to determine whether net income is higher or lower than \$74,914, but rather if it is “different”. That makes this a 2-tail test since the change is ambiguous and could mean it is either higher or lower than \$74,914.H0:= \$74,914Ha: \$74,914Step 2: Since we’re testing for a population mean and the sample size is 30 or greater, we can use the normal (Z) distribution. There is no mention of a population size so we don’t have to worry about the finite correction factor (FCF). Z = Step 3: α = .05
Module 14: Hypothesis Testing for Single Populations Part 1I.Hypothesis Testing for a Single Population Mean, Large Sample Size (n 30)Example 1:A nationwide survey of CPAs found that the average net income for sole practitioner CPAs was \$74,914. A believes this figure does not apply to sole practitioner CPAs in the state of South Dakota. The researcher takes a random sample of 112 sole practitioner CPAs in South Dakota which results in a sample mean net income of \$78, 695 with a sample standard deviation of \$14,530. At the .05 level of significance, test to determine if the mean net income of sole practitioner CPAs in South Dakota is different from the national average.

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