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Unformatted text preview: CHAPTER F ORMULAS Steps of Hypothesis Testing 1. 2. Develop the null and the alternative hypotheses.
Determine the critical value or values of t or Z at speciﬁed level of signiﬁcance 0:.
Compute the test statistic t or Z from the sample data. Compare the test statistic (from step 3) to that of the critical value or values (from
step 2). If the test statistic is beyond the critical value or values, reject the null
hypothesis. If you are using the p-value method, reject the null hypothesis if the p-value is less than 11. Draw conclusions and report your results. Hypothesis Test Situations Hypothesis Tests about a Population Mean: Large Sample (11 2 30) . . X —
Test Statistic: Z = “0 (o Assumed Known) (9.1)
If 0' is not known, substitute S for 0' in computing the Z statistic. Thus:
. . . _ La, .
Test Statlstlc. Z —- (0' estimated by S) (9.2) s/JH Decision Rules for Hypothesis Testing When Using the P-Value Method, In All Cases Reject Ho if P-Value < a A. Lower one-tailed test of the form
H03 ll 2 l1 0
Ha: [>1 < #0 Reject Ho if Z < -Z0t II. III. CHAPTER FORMULAS
(Continued) B. Upper one-tailed test of the form
H03 lL1 E P1 0
Ha: I-1 5 Po
Reject H0 ifZ > ZDt
C. Two-tailed test of the form
Ho: H = H 0
Ha: t1 i H o
Reject H0 ifZ < -Zw,2 or Z > sz Hypothesis Tests about a Population Mean: Small Samples (11 < 30) and
Unknown 0' . . . i —
Standardized Test Statlstlc: t : p" (9.8)
The decision rules are the same as those shown in Part I with the t statistic
substituted for the Z statistic.
Hypothesis Tests about a Population Proportion
Standardized Test Statistic: Z = p _ p” (9.9)
where 01—) = M (9.10)
n The decision rules are the same as those shown in Part I. In the formulation of
hypotheses, substitute p for p. CHAPTER FORMULAS
(continued) Determining the Sample Size for a Hypothesis Test about a Population Mean Recommended Sample Size for a One-Tailed Hypothesis Test (9.13) where z0L = Z value associated with an area of at in one tail of the distribution
Zﬁ = Z value associated with an area of [3 in one tail of the distribution 0' = the standard deviation of the population
no = the value of the population mean in the null hypothesis pa = the actual value of the population mean in the statement about a
Type II error In a two-tailed test, replace ZDI with Zaﬂ . ...
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This note was uploaded on 02/24/2012 for the course BUSINESS 281 taught by Professor Gray during the Spring '12 term at Florida State College.
- Spring '12