Homework Answers
Solution:
Given:
p = 0.07
n = 1000
x = Number of a's in sample of 1000 letters = 84
Thus sample proportion of a's is:
Level of significance = 
Hypothesis:
We have to find z test statistic:
Find critical values:
use level of significance = 
Since this is two tailed, we find : Area = 
Look in z table for area = 0.0250 or its closest area and find z value
Area 0.0250 corresponds to -1.9 and 0.06
thus z critical value = -1.96
Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96)
Decision Rule:
Reject null hypothesis ,if z test statistic value < z
critical value=-1.96 or z test statistic value > z
critical value= 1.96 , otherwise we fail to reject H0.
Since z test statistic value = z = 1.74 is neither less -1.96 , not greater than 1.96, we failed to reject H0.
Conclusion:
At 0.05 level of significance , we do not have sufficient evidence to conclude that the proportion of a's has changed in modern times.
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