One-Sample t test Worksheet 3 - ANSWER KEY

One-Sample t Test Example 4 (Commuter Students) – ANSWER KEY Kennesaw State University has a large number of commuter students The registrar wants to determine whether KSU students differ in the number of miles they drive to school compared to the national average ( Step 1 State your hypotheses a Is it a one-tailed or two-tailed test? Two-tailed b Research hypotheses HA: KSU students differ in the number of miles driven to school compared to the national average H0: KSU students do not differ in the number of miles driven to school compared to the national average c Statistical hypotheses HA:  ksu  16 H0:  ksu 16 Step 2 Set the significance level   = 05 Determine tcrit tcrit = + 2.262 Step 3 Select and compute the appropriate statistical test Miles Commuted X 10 5 22 4 15 5 7 9 3 20 ΣX = 100 X X–X 10 0 -5 12 -6 5 -5 -3 -1 -7 10 (X – X )2 0 25 144 36 25 25 9 1 49 100 414 s 2 X X  X   n 1 414  10  1  414 9 s x2 46 2 s X2 sX  n  46 10  4.6 s X 2.145 tobt  X  sX 10  16  2.145   6 2.145 tobt  2.80 Step 4 Make a decision Determine whether the value of the test statistic is in the critical region Draw a picture Label tcrit and tobt Is tobt in the critical region? Yes Should you reject or retain the H0? Reject tobt = -2.80 tcrit = -2.262 tcrit = +2.262 Step 5 Report the statistical results t(9) = -2.80, p < 05 Step 6 Write a conclusion KSU students (M=10) drive fewer miles to school than the national average (μ = 16) Step 7 Compute the estimated d estimated d  X   10  16 6    88 sX 6.782 6.782 Step 8 Compute r2 and write a conclusion t2  2.80 2 7.84 7.84 r  2    .4656 2 t  df  2.80  9 7.84  9 16.84 2 The fact that the sample consists of KSU students accounts for 47% of the variance in miles driven to school  ...Is tobt in the critical region? Yes Should you reject or retain the H0? Reject tobt = -2 .80 tcrit = -2 .262 tcrit = +2.262 Step Report the statistical results t( 9) = -2 .80, p < 05 Step Write a... KSU students (M=10) drive fewer miles to school than the national average (μ = 16) Step Compute the estimated d estimated d  X   10  16 6    88 sX 6.782 6.782 Step Compute r2 and write... a conclusion t2  2.80 7.84 7.84 r     .4656 t  df  2.80  7.84  16.84 The fact that the sample consists of KSU students accounts for 47% of the variance in miles driven to school