SOLUTION: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) Construct hypotheses appropriate for the fol
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Question 1157910: It is believed that nearsightedness affects about 8% of all children. In a random sample of 194 children, 21 are nearsighted.
(a) Construct hypotheses appropriate for the following question: do these data provide evidence that the 8% value is inaccurate?
a.(Ho: p = .08
Ha: p > .08)
b.(Ho: p = .08
Ha: p ≠ .08)
c.(Ho: p = .08
Ha: p < .08)
(b) What proportion of children in this sample are nearsighted?
______ (round to four decimal places)
(c) Given that the standard error of the sample proportion is 0.0195 and the point estimate follows a nearly normal distribution, calculate the test statistic (use the Z-statistic).
Z = _____(please round to two decimal places)
(d) What is the p-value for this hypothesis test?
p = ____ (please round to four decimal places)
(e) What is the conclusion of the hypothesis test?
a)Since p ≥ α we accept the null hypothesis
b)Since p ≥ α we do not have enough evidence to reject the null hypothesis
c)Since p<α we fail to reject the null hypothesis
d)Since p ≥ α we reject the null hypothesis and accept the alternative
e)Since p<α we reject the null hypothesis and accept the alternative
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
b. When Ho is p1=p2, I want Ha to be everything else, which is p1 NE p2
c. It is 21/194 or 0.1082
d. this is (0.1082-.080/0.0195, The difference of means divided by the SE. It is 1.45.
The p-value is 0.1470
e. This means that such a result could happen by chance 0.1470 of the time if the true value were 0.08. We fail to reject Ho because the p-value is greater than alpha. That is b. We don't accept the null hypothesis but rather say we are unable to reject it. Not guilty vs, innocent analogy.
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