You can be 90 percent confident that Brand A cereal has between 2.81 fewer and 19.81 more raisins per box than Brand B. According to Table 3 in 'Statistics Tables,' the critical value for t. A 90 percent confidence interval is equivalent to an alpha level of 0.10, which is then halved to give 0.05. The degrees of freedom is the smaller of (6 – 1) and (9 – 1), or 5. The difference between and is 102.1 – 93.6 = 8.5. The degrees of freedom parameter for looking up the t‐value is the smaller of n 1 – 1 and n 2– 1.Įstimate a 90 percent confidence interval for the difference between the number of raisins per box in two brands of breakfast cereal. Where a and b are the limits of the confidence interval, and are the means of the two samples, is the value from the t‐table corresponding to half of the desired alpha level, s 1and s 2 are the standard deviations of the two samples, and n 1and n 2are the sizes of the two samples. This test has not provided statistically significant evidence that intensive tutoring is superior to paced tutoring. The computed t of 1.166 does not exceed the tabled value, so the null hypothesis cannot be rejected. 05,9in the t‐table (Table 3 in 'Statistics Tables'), which gives a critical value of 1.833. Because this is a one‐tailed test, the alpha level (0.05) is not divided by two. The degrees of freedom parameter is the smaller of (12 – 1) and (10 – 1), or 9. Two randomly chosen groups are tutored separately and then administered proficiency tests. The number of degrees of freedom for the problem is the smaller of n 1– 1 and n 2– 1.Īn experiment is conducted to determine whether intensive tutoring (covering a great deal of material in a fixed amount of time) is more effective than paced tutoring (covering less material in the same amount of time). Where and are the means of the two samples, Δ is the hypothesized difference between the population means (0 if testing for equal means), s 1 and s 2are the standard deviations of the two samples, and n 1and n 2are the sizes of the two samples. Requirements: Two normally distributed but independent populations, σ is unknown Two Sample t test for Comparing Two Means

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