Rosner analyzed data from children who lived near a lead smelter (which is a facility that uses extreme heat to extract the metal lead from lead ore) in El Paso, Texas, and reported that out of 124 children studied, 23 developed colic (which is a pattern of fussiness and crying for no apparent reason). Suppose that in the state of Taxes in general at the time (early 1980s), the rate of colic in children was 16.0%. Follow the steps for testing whether the proportion of children developing clico was significantly different for the 124 children living near the lead smelter than for Taxes children in general (16%).
Rosner analyzed data from children who lived near a lead smelter (which is a facility that uses extreme heat to extract the metal lead from lead ore) in El Paso, Texas, and reported that out of 124 children studied, 23 developed colic (which is a pattern of fussiness and crying for no apparent reason). Suppose that in the state of Taxes in general at the time (early 1980s), the rate of colic in children was 16.0%.
Follow the steps for testing whether the proportion of children developing clico was significantly different for the 124 children living near the lead smelter than for Taxes children in general (16%).
Use alpha level of 0.03
a. Identify the null hypothesis for this statistical test.
b. Identify the alternative hypotheses for this statistical test.
c. Explain: Why should this be a two-tailed test, the way I have described it?
d. calculate the sample proportion p̂, rounded to three decimal places.
e. Calculate the appropriate test statistic, show all work.
f. Based on the test statistic you calculated above and the fact that this is a two-tailed test, provide the appropriate p-value.
g. Considering that your alpha level is 0.03, what do you conclude? Include whether you reject or fail to reject the null hypothesis, and also what you conclude about the colic proportion.
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