Hypothesis Test for a Population Proportion

4.44 Nearsighted: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?

• Ho: p = .08 Ha: p > .08
• Ho: p = .08 Ha: p < .08
• 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-value =(please round to three decimal places)

(e) What is the conclusion of the hypothesis test?

• Since p we reject the null hypothesis and accept the alternative
• Since p we accept the null hypothesis
• Since p< we reject the null hypothesis and accept the alternative
• Since p< we fail to reject the null hypothesis
• Since p we do not have enough evidence to reject the null hypothesis

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