t Test - Homework Assignment ANSKEY

xlsx

School

Stony Brook University *

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467

Subject

Statistics

Date

Feb 20, 2024

Type

xlsx

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Uploaded by EarlTeamLoris36

MY CALCULATIONS . . . 9.02 7 Urgent Emergency 29 33 30 43 xbar (U) 30.1666666666667 32 26 xbar (E) 33.225 31 46 xbar (U) - xbar (E) 3.05833333333333 22 31 s (U) 5.65736220569594 26 40 n (U) 30 30 34 S.E. 1.03288829867895 38 4 t-statistic 2.96095263858144 29 30 p 0.006060490857198 28 24 29 40 38 32 30 36 43 31 23 45 32 20 25 31 32 42 30 29 32 40 35 34 34 44 29 9 21 25 29 29 31 34 36 28 14 37 31 18 t -Test for a priori hypothetical values (golden standard) of the origina As the p-value is less than .05, we REJECT the null hypothesis (H0). While these Emergency data represent hypothetical observations, it depends on your hypothesis. According to question 9.02 #7 on page 317, the hypothesis assumes equal variance…

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DATA ANALYSIS USING EXCEL . . . Urgent Mean 30.1666666666667 Variance 32.0057471264368 Observations 30 Pearson Correlation -0.157204637669349 Hypothesized Mean Difference 0 df 29 t Stat -0.720259588596404 P(T<=t) one-tail 0.238565464993905 t Critical one-tail 1.6991270265335 P(T<=t) two-tail 0.477130929987811 t Critical two-tail 2.0452296421327 In this case, n1 = n2 al sample t-Test: Paired Two Sample for Means - Use When Sample Sizes Are the As the p-value is greater than .05, we DO NOT REJECT the null hypothesi However, these two samples do not have the same population because I omitted 10 Emergency observations!! In this case, we should use a t Test using Variances!

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DATA ANALYSIS USING EXCEL . . . Using Pooled Variance . . . Emergency Urgent Emergency 31.7666666666667 Mean 30.1666666666667 33.225 98.3919540229885 Variance 32.0057471264368 91.35833333 30 Observations 30 40 Pooled Variance **66.0462009803922 Hypothesized Mean Difference 3.058333333 df 68 t Stat -3.1162514671101 P(T<=t) one-tail 0.001341412662326 t Critical one-tail 1.66757228079671 P(T<=t) two-tail 0.002682825324651 t Critical two-tail 1.99546893142984 Same! t-Test: Two-Sample Assuming Unequal Variances - Use When Sample Sizes Are As the p-value is less than .05, we REJECT the null hypothesis (H0). is (H0). Especially, when the "hypothesized" mean difference is 3.05833333 **Please note that the pooled variance is multipliedby 0.5.

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So when do we use a t test for Equal Variance? This is when we employ the F Test! VAR1/VAR2 = 0.350331994451557 e Different! Remember when the F Test equals 1, then there is an asssumption of Equal Variance!!

t-Test: Two-Sample Assuming Equal Variances Urgent Emergency Mean 30.166666667 33.225 Variance 32.005747126 91.35833333 Observations 30 40 Pooled Variance 66.04620098 Hypothesized Mean Difference 0 df **68 t Stat -1.558125734 P(T<=t) one-tail 0.0619228693 t Critical one-tail 1.6675721781 P(T<=t) two-tail 0.1238457385 t Critical two-tail 1.9954677555 **Please note that the degrees of freedom are n1 - 1 and n2 -1 combined! As the p-value is less than .05, we DO NOT reject the null hypothesis (H0).

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