Question

A recent study examined hearing loss data for 1822 U.S. teenagers. In this sample, 343 were found to have some level of hearing loss. News of this study spread quickly, with many news articles blaming the prevalence of hearing loss on the higher use of ear buds by teens. At MSNBC.com (8/17/2010), Carla Johnson summarized the study with the headline: "1 in 5 U.S. teens has hearing loss, study says." To investigate whether this is an appropriate or a misleading headline, you will conduct a test of significance with the following hypotheses: Null: п-0.20 Alternative : п # 0.20 Use the Theory-Based Inference applet to determine a p-value. Round your answer to 4 decimal places, e.g. 0.7534. Answer *1: the absolute tolerance is/-0.0002 Based on your p-value, there is strong evidence that the proportion of all U.S. teens with some hearing loss is different than 1 in 5 (or 20%) True С False

Answer 1

Ans:

1)Test statistic:

z=(0.1883-0.2)/SQRT(0.2*(1-0.2)/1822)

z=-1.253

p-value=2*P(z<-1.253)=0.2102

2)As,p-value>0.05,we fail to reject H₀.

There is not sufficient evidence that proportion is different from 0.2.

False

3)

95% confidence interval for p

=0.1883+/-1.96*sqrt(0.1883*(1-0.1883)/1822)

=0.1883+/-0.0180

=(0.1703, 0.2062)

4)

Margin of error=0.0180

5)

True,0.20 is the plausible value,as 0.20 is included within the interval.

6)

True.