1. The stress levels of 30 unemploved laborers were measured by a questionnaire
ID: 3050586 • Letter: 1
Question
1. The stress levels of 30 unemploved laborers were measured by a questionnaire before and after a real iob interview. The stress level rose from a mean of 63 points to a mean of 71 points. The (unbiased) standard deviation of the difference scores was 18. a. What is the appropriate null hypothesis b. What is the critical value of t for a .05, c. What is the observed (i.e., calculated) d. What is your statistical decision with for this example two-tailed test? value of t? respect to the null hypothesis? e. Given your conclusion in part d, could you be making a Type I or Type II error?Explanation / Answer
Here define variable X as stress score before real job interview and Y as stress score after real job interview.
Define 1 and 2 as mean stress score before and after real job interview, then it is given that corresponding sample means scores are Xbar = 63 and Ybar = 71. Futher it is also given sample standard deviation of difference in scores = sd=18.
Then
a) The null hypothesis as H0 : 1 = 2
b) Critical value of t for = 0.05 two sided P[T > Tcritical ] =0.05 where degrees of freedom of T are n-1
It gives critical value = 2.04523 for 29 DF and = 0.05
c) Observed value of T = n * (Xbar-Ybar)/sd = 30 *(63-71)/18 = -2.43432
Absolute value of T observed is = 2.43432
d) Observed T value > Critical T value implies that null hypothesis may be rejected.
e) Here Type I error is fixed as 0.05 and therefore we are committing Type II error.
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