Question

A study that evaluated the effects of a reduction in exposure to traffic-related air pollutants compared respiratory symptoms of 281 residents of an area with congested streets with 168 residents in a similar area where the congestion was removed because a bypass was constructed. The symptoms of the residents were evaluated at baseline and again a year after the bypass was completed. For the residents of the congested streets, 16 reported that their symptoms of wheezing improved between baseline and one year later, while 35 of the residents of the bypass streets reported improvement.

Find the test statistic. Construct a sketch of the distribution of the test statistic under the assumption that the null hypothesis is true. Find the P-value and use your sketch to explain its meaning. (Use α = 0.01. Use the pooled estimate in your calculations. Round your value for z to two decimal places, and round your P-value to four decimal places.)

z=

p-value=

Use a 95% confidence interval to answer this question. (Round your answers to four decimal places.)

Answer 1

We conduct Z-test for two proportions as :

Hence, we conclude that there is a reduction in respiratory symptoms for area where the congestion was removed as compared to area with congested streets at 1 % level of significance.

Now,

95% confidence interval is : ( - 0.2181 , - 0.0839 )

Since, the 95% confidence interval does not include 0 value , we can say that there is a reduction in respiratory symptoms for area where the congestion was removed as compared to area with congested streets at 5 % level of significance.