One study, based on responses from 1,024 randomly selected teenagers, concluded
ID: 3126945 • Letter: O
Question
One study, based on responses from 1,024 randomly selected teenagers, concluded that 39% of teenagers cite grades as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in the population feel that grades are their greatest source of pressure.
a) Write the claim mathematically and identify Ho and Ha.
(b) Find the critical value(s) and identify the rejection region(s). (c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the nullhypothesis, and (e) interpret the decision in the context of the original claim.
Explanation / Answer
H0: p =0.5
Ha: p <0.5
Left tailed test
STd dev = rt of p(1-p) = 0.5
Std error = 0.5/rt 1024 =0.0156
p diff = 0.39-0.5 = -0.11
z statistic = -0.11/0.0156
=-7.04
The P-Value is < 0.00001.
The result is significant at p < 0.05.
Reject null hypothesis.
Hence there is statistical evidence to claim that Ha is true.
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