Question

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? ОНо: р 3D.08 На: р 2 .08 Ho: p .08 На: р < .08 Ho: p .08 На: р > .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) (please round to two decimal places) Z=

Answer 1

a )

H0: p = 0.08

Ha: p $\neq$ 0.08

b)

sample proportion $\hat{p}$ = 21 / 194 = 0.1082

c)

Test statistics

z = ($\hat{p}$ - p) / SE

= (0.1082 - 0.08) / 0.0195

= 1.45

d)

p-value = 2 * P(Z > z)

= 2 * P(Z > 1.45)

= 2 * 0.0735

= 0.1470

e)

Since p >= $\alpha$ , we do not have enough evidence to reject the null hypothesis.