On the basis of her newly developed technique, a student believes she can reduce
ID: 3200433 • Letter: O
Question
On the basis of her newly developed technique, a student believes she can reduce the amount of time schizophrenics spend in an institution. As director of training at a nearby institution, you agree to let her try her method on 17 schizophrenics, randomly sampled from your institution. The mean duration that schizophrenics stay at your institution is 85 weeks, with a standard deviation of 12 weeks. The scores are normally distributed. The results of the experiment show that the patients treated by the student stay a mean duration of 80 weeks, with a standard deviation of 20 weeks.
(c) What do you conclude about the student's technique? Use = 0.052 tail.
zobt =
zcrit = ±
Explanation / Answer
Solution:-
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: = 85
Alternative hypothesis: 85
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the sample mean is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.052. The test method is a one-sample t-test.
Analyze sample data. Using sample data, we compute the standard error (SE),z statistic test statistic (z).
SE = s / sqrt(n), s = 20
S.E = 4.85071
z = (x - ) / SE
z = - 1.03078
z critical = + 1.943
Rejection region is - 1.943 > z >1.943
where s is the standard deviation of the sample, x is the sample mean, is the hypothesized population mean, and n is the sample size.
Interpret results. Since the z-value (1.031) lies within acceptance region so we have to accept the null hypothesis.
From this we can conclude that the mean we get from the student's technique is same as the mean for the instutution.
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