The researchers are interested in examining if differences exist between the sam
ID: 3151445 • Letter: T
Question
The researchers are interested in examining if differences exist between the sample mean (M= 15) of a group of individuals who receive corrective eye surgery on a vision test versus individuals from the population who do not have corrective eye surgery on the same vision test. The researchers know the population vision test average for individuals without corrective surgery (=10) and the standard error (M= 3). Conduct the One Sampled z-¬test and test the calculated statistic for significance using a two-¬tailed significance test with an alpha level of .05 (5%).
Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 10
Ha: u =/ 10
As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.05 ,
alpha/2 = 0.025
zcrit = +/- 1.959963985
Getting the test statistic, as
X = sample mean = 15
uo = hypothesized mean = 10
se = standard error = 3
Thus, z = (X - uo) / se = 1.666666667
Also, the p value is
p = 0.095580705
As z < 1.96, and P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant difference between that vision test average between those with and without corrective eye surgery at 0.05 level. [CONCLUSION]