Is this test right, left, or two tailed?.What are the null and alternative hypotheses? Write the null and alternative hypotheses in words and in symbols.Which distribution do you use to perform the test?.Are the population standard deviations known or unknown?.Is this a test of two means or two proportions?.Is there a difference in the weighted alpha of the top 30 stocks of banks in the northeast and in the west? Test at a 5% significance level. Where s p o o l e d = ( n 1 – 1 ) s 1 2 + ( n 2 – 1 ) s 2 2 n 1 + n 2 – 2 Cohen's Standard Effect Sizes Size of effectĬohen's d is the measure of the difference between two means divided by the pooled standard deviation: d = x ¯ 1 – x ¯ 2 s p o o l e d The calculated value of effect size is then compared to Cohen’s standards of small, medium, and large effect sizes. Cohen’s d, named for United States statistician Jacob Cohen, measures the relative strength of the differences between the means of two populations based on sample data. The evidence shows that the mean of the final exam scores for the online class is lower than that of the face-to-face class.Īt the 5% level of significance, from the sample data, there is (is/is not) sufficient evidence to conclude that the mean of the final exam scores for the online class is less than the mean of final exam scores of the face-to-face class.Ĭohen's Standards for Small, Medium, and Large Effect Sizes Cohen's d is a measure of effect size based on the differences between two means. H a: μ 1
H 0: μ 1 = μ 2 Null hypothesis: the means of the final exam scores are equal for the online and face-to-face statistics classes.Make a decision: Since α > p-value, reject H 0. Half the p-value is below –1.2 and half is above 1.2. Do not pool the variances.Ĭalculate the p-value using a Student’s t-distribution: p-value = 0.0054 Using a calculator, df is approximately 18.8462. Since there are no other words to indicate H a, assume it says “is different.” This is a two-tailed test.ĭistribution for the test: Use t df where df is calculated using the df formula for independent groups, two population means. The words “the same” tell you H 0 has an “=”. = difference in the sample mean amount of time girls and boys play sports each day. This is a test of two independent groups, two population means.
Then, μ g is the population mean for girls and μ b is the population mean for boys. Let g be the subscript for girls and b be the subscript for boys. The population standard deviations are not known.
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