The instructions are as follows: -Write all given values -State the null and alt
ID: 3379089 • Letter: T
Question
The instructions are as follows:
-Write all given values
-State the null and alternative hypotheses
-Determine the level of significance,
-Determine the approproiate test statistic to be used and compute
-Determine the critical region and find its value
-Write your decision whether to reject or do not reject the null hypothesis, state your interpretation
The average height of females in the freshman class of a certain college has historically been 162.5 centimeters with a standard deviation of 6.9 centimeters. Is there reason to believe that there has been a change in the average height if a random sample of 50 females in the present freshman class has an average height of 165.2 centimeters? Use 0.05 level of significance. (13pts) 1.Explanation / Answer
Formulating the null and alternative hypotheses,
Ho: u = 162.5
Ha: u =/ 162.5 [ANSWER, HYPOTHESES]
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As we can see, this is a two tailed test.
Thus, getting the critical z, as alpha = 0.05 [SIGNIFICANCE]
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Getting the test statistic, as
X = sample mean = 165.2
uo = hypothesized mean = 162.5
n = sample size = 50
s = standard deviation = 6.9
Thus, z = (X - uo) * sqrt(n) / s = 2.766939579 [ANSWER, TEST STATISTIC]
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alpha/2 = 0.025
zcrit = +/- 1.959963985
Thus, the critical region is z < -1.959963985 or z > 1.959963985. [CRITICAL REGION]
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As z > 1.959963985, we REJECT THE NULL HYPOTHESIS.
Thus, there is significant evidence that there is a change in the avergae height of females in the freshman class. [CONCLUSION]
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