MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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Question
In a two-sided test: (H₁: μ ‡ claimed value or Ho:p ‡ claimed value) If the statement of the problem does not indicate which alternate hypothesis to use then run a two-sided test. 2. Identify the significance level (c). If the problem does not give one then take a = 0.5 3. Find the critical value. You need to determine if you are using a Z dsitribution (proportions or mean where is known) or the t-distribution (mean where you approximate with s). For a left sided test: CV = invNorm(a) or invT(α, n-1) where n is the sample size (n-1 = degrees of freedom). For a right sided test: CV = invNorm(1-x) or invT(1-a, n-1) where n is the sample size (n-1 = degrees of freedom). For a two-sided test: CV's (there are TWO) = + invnorm() or invT(n-1)where n is the sample size (n-1 = degrees of freedom). 4. Find the test statistic For means: Z = or t = where is the assumed parameter in the null hypothesis. Vi For proportions: Z=-, where p is the assumed parameter in the null hypothesis. DI V 5. Find the p-value For left-sided test: normalcdf(-10000000000000, Z, 1, 0) or tcdf(-1000000000000, t, n-1) For right-sided test: normalcdf(Z,100000000000000, 1, 0) or tcdf(t,1000000000000000, n-1) For two-sided test: = 2*normalcdf(-100000000000000, -Z, 1, 0) or 2*tcdf(-100000000000000, -t, n-1) where -Z (or -t) is the negative version of the test statistic (regardless if the test statistic is negative or positive). NOTE: The tests 1-PropZTest, TTest, and ZTest will calculate both the test statistic and p-value for you. 6. Make a conclusion: If p-value <a or if the test statistic is further from the mean then the critical value (so the test statistic is in the rejection region) then reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Problem: Find the p-value if left-sided test, t-distribution, n = 45, Test Statistic = -2.5
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Transcribed Image Text:In a two-sided test: (H₁: μ ‡ claimed value or Ho:p ‡ claimed value) If the statement of the problem does not indicate which alternate hypothesis to use then run a two-sided test. 2. Identify the significance level (c). If the problem does not give one then take a = 0.5 3. Find the critical value. You need to determine if you are using a Z dsitribution (proportions or mean where is known) or the t-distribution (mean where you approximate with s). For a left sided test: CV = invNorm(a) or invT(α, n-1) where n is the sample size (n-1 = degrees of freedom). For a right sided test: CV = invNorm(1-x) or invT(1-a, n-1) where n is the sample size (n-1 = degrees of freedom). For a two-sided test: CV's (there are TWO) = + invnorm() or invT(n-1)where n is the sample size (n-1 = degrees of freedom). 4. Find the test statistic For means: Z = or t = where is the assumed parameter in the null hypothesis. Vi For proportions: Z=-, where p is the assumed parameter in the null hypothesis. DI V 5. Find the p-value For left-sided test: normalcdf(-10000000000000, Z, 1, 0) or tcdf(-1000000000000, t, n-1) For right-sided test: normalcdf(Z,100000000000000, 1, 0) or tcdf(t,1000000000000000, n-1) For two-sided test: = 2*normalcdf(-100000000000000, -Z, 1, 0) or 2*tcdf(-100000000000000, -t, n-1) where -Z (or -t) is the negative version of the test statistic (regardless if the test statistic is negative or positive). NOTE: The tests 1-PropZTest, TTest, and ZTest will calculate both the test statistic and p-value for you. 6. Make a conclusion: If p-value <a or if the test statistic is further from the mean then the critical value (so the test statistic is in the rejection region) then reject the null hypothesis. Otherwise, fail to reject the null hypothesis. Problem: Find the p-value if left-sided test, t-distribution, n = 45, Test Statistic = -2.5
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