stat exam 3 study guide

# One sample t test normally distrib pop standard dev

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ONE SAMPLE T-TEST : NORMALLY DISTRIB. POP.; STANDARD DEV. UNKNOWN (POPULATION MEAN) t = x bar – delta divided by s/sqrt of n

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x bar sample mean ; delta specified value to be tested ; s sample standard deviation ; n sample size degrees of freedom (df) values in t-table listed by df; df = n – 1 variance = subtract mean from each number and square the results. Average out these numbers (standard dev is square root of result) STEPS: 1. Computer sample mean and sample standard deviation. 2. Compute t value. 3. Compare t value to critical value in table. 4. Critical value = t significance level, df (total in data set minus one) 5. Null hypothesis is rejected if t value > t critical OR p value < alpha ONE SAMPLE Z-TEST : NORMALLY DIST. POP. ; STANDARD DEV. KNOWN - z = x bar – delta divided by pop standard dev./sqrt of n - x bar sample mean ; delta specified value to be tested ; n sample size - STEPS: 1. Compute z value; 2. Find tables value for z (z that is less than or equal to the z value) ; 3. Subtract tabled z value from 1 (this gets you your p- value) ; 4. Reject null hypothesis if p value is less than significance level) TWO SAMPLE Z-TEST FOR COMPARING TWO MEANS : TWO NORMALLY DISTR. BUT INDEPENDENT POP.; STANDARD DEV. IS KNOWN - z = sample mean 1 – sample mean 2 – delta divided by the square root of standard dev. 1 / sample size 1 plus standard dev. 2 / sample size 2 - DELTA IS ZERO WHEN TESTING FOR EQUAL MEANS - STEPS: 1. compute z value (z score). 2. Find corresponding area on table 3. Multiply this area by 2 for p value. 4. If p value is less than significance level (which if not given is always .05) then the null hypothesis is rejected TWO SAMPLE T-TEST FOR COMPARING TWO MEANS: TWO NORMALLY DISTR. BUT INDEPENDENT POP; STANDARD DEV. IS UNKNOWN - t = sample mean 1 – sample mean 2 – delta divided by the square root of sample standard dev. 1 / sample size 1 plus sample standard dev. 2 / sample size 2 - the number of degrees of freedom (df) is the smaller of sample size 1 – 1 and sample size 2 – 1 - STEPS: 1. Compute t value. 2. Look up t critical value for significance level, df. 3. If t value is > t critical then the null hypothesis is rejected - IF GIVEN A CONFIDENCE INTERVAL KNOWN THAT: CONFIDENCE INTERVAL + SIGNIFICANCE LEVEL = 1 Not Reject Null Hypothesis Reject Null Hypothesis True CORRECT Type I Error False Type II Error CORRECT TO FIND CRITICAL VALUE FIND SIGNIFICANCE LEVEL DIVIDED BY 2 ON CHART AND ADD NUMBER AT TOP TO NUMBER TO THE LEFT PROPORTIONS - P hat = x/n -
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