Analyses of drinking water samples for 100 homes in each of twodifferent sections of a city gave the following means and standarddeviations of lead levels (in parts per million).
| section 1 | section 2 |
| sample size | 100 | 100 |
| mean | 34.5 | 36.2 |
| standard deviation | 5.8 | 6.0 |
(a) Calculate the test statistic and itsp-value to test for a difference in the two population means. (UseSection 1 ? Section 2. Round your test statistic to two decimalplaces and your p-value to four decimal places.)
z =
p-value =
Use the p-value to evaluate the statistical significance of theresults at the 5% level.
a. H0 is not rejected. There is sufficient evidence to indicatea difference in the mean lead levels for the two sections of thecity.
b. H0 is rejected. There is sufficient evidence to indicate adifference in the mean lead levels for the two sections of thecity.
c. H0 is rejected. There is insufficient evidence to indicate adifference in the mean lead levels for the two sections of thecity.
d. H0 is not rejected. There is insufficient evidence toindicate a difference in the mean lead levels for the two sectionsof the city.
(b) Calculate a 95% confidence interval toestimate the difference in the mean lead levels in parts permillion for the two sections of the city. (Use Section 1 ? Section2. Round your answers to two decimal places.)
parts per million______ to________parts per million
(c) Suppose that the city environmentalengineers will be concerned only if they detect a difference ofmore than 5 parts per million in the two sections of the city.Based on your confidence interval in part (b), is the statisticalsignificance in part (a) of practical significance to the cityengineers? Explain.
a. Since all of the probable values of ?1 ? ?2 given by theinterval are all less than ?5, it is likely that the differencewill be more than 5 ppm, and hence the statistical significance ofthe difference is of practical importance to the the engineers.
b. Since all of the probable values of ?1 ? ?2 given by theinterval are all greater than 5, it is likely that the differencewill be more than 5 ppm, and hence the statistical significance ofthe difference is of practical importance to the the engineers.
c. Since all of the probable values of ?1 ? ?2 given by theinterval are between ?5 and 5, it is not likely that the differencewill be more than 5 ppm, and hence the statistical significance ofthe difference is not of practical importance to the theengineers.
