Question

PSYC371 Calculating the INDEPENDENT-samples t-statistie' 15 points Assignment #11 PROBLEM: A scientist would like to know if sleeping in a room with a night light on will affect quality of sleep. The table shows hourly nights of quality sleep reported by two independent groups in the experiment. Participants were randomly assigned to either the 'light' or 'NO Light' conditions. Light - 6 6 7 7 score minus mean score minus mean squared 7-6.55 0.45 0. 20.2029 6-6.5 = "0.95 -0.52 0.102 6-6.53 = -0.55 -0.55² = 0.1025 5-6.35€ -1.5 -1.55 = 2.4025 -6.55 0.45 0.45 0.202. -655 0.45 0.2025 -6.55 = 1.45 11.452.2.1025 -6-55 0.45 0.45 0.2025 -6-555-0-55 9.532 70.3023 SS, -6.2225 7 2 8 7 6 81 7 6 Sum 59 Mean 6.55 df, 8 Note: df - 1 NO Light 8 6 5 6 - 5- 5- score minus mean score minus mean squared 8-6-1 = 1.840.89 3.5721 3-6-3-. 1 .2321 6-6-11 -01 -0. 1 9 .121 5 -60-I01 .2321 6-6.11=-gell 10.4² = 0.0121 - 5-6.11 -1.1 -1. 1.232 5-611 L Hol = 1.1321 12-611 = 0.89 0.89 = 9.792 6-6.11 - 1.89 1-812 = 3.5721 SS, - 12.8589 8. Sum Mean II - 4 a. Compute the pooled variance and SS for the scores. 131 - 6.2225 + 12.8889 8 +8 $ .$5+ , Sum of squares formula: s8 - dfdf, X2 19.114 - 11. 1944

Answer 1

a) pooled variance and SS for the scores; s? = 1.194463 Solution: Light 7 6 6 5 7 7 8 7 6 (score -mean) (score-mean)^2 0.444444444 0.197530864 -0.555555556 0.308641975 -0.555555556 0.308641975 -1.555555556 2.419753086 0.444444444 0.197530864 0.444444444 0.197530864 1.444444444 2.086419753 0 .444444444 0.197530864 -0.555555556 0.308641975 SS1 = 6.2225 b) Estimated standard error is; Sim1-mz) 0.515205 c) t test statistics value is given as; 0.862656 Sum The critical value at 5% and d.f = 16 for two tailed from t dist is given as, t critical value => 2.1200 Mean = 6.555556 n1 = 9 df1 =8 d) Cohen d value is; d => 0.40666 The null hypothesis state that there is no difference between lighting condition. The alternative hypothesis state that there is difference between lighting condition. Since the critical value is greater than test statistic value, therefore we fail to reject null hypothesis, and we conclude that there is no difference between lighting condition.

No Light (score -mean) (score-mean)^2 8 1.888888889 3.567901235 5 -1.111111111 1.234567901 -0.111111111 0.012345679 5 -1.111111111 1.234567901 -0.111111111 0.012345679 5 -1.111111111 1.234567901 51 -1.111111111 1.234567901 7 0.888888889 0.790123457 8 1.888888889 3.567901235 SS2 =12.8889 6.111111 n2 = 9 df2=8 Sum= Mean =