>> Applied Statistics
Use the data in
[a] Construct a 95% confidence interval for the proportion of mothers who smoke.
[b] What sample size would be required to estimate this proportion to within 0.02 of the population proportion with 95% confidence if no prior bounds are used. What is this sample size if the sample proportion from part a is used as the prior bound?
[c] Construct a 90% confidence interval for the mean birth weight of newborns with mothers who smoke. Do the same for mothers who don't smoke.
[d] Use this data as a preliminary sample to determine the sample size required to estimate the mean birth weight for mothers who smoke to within 0.5 with 99% confidence. Do the same for mothers who don't smoke.
[e] Construct a 90% confidence interval for the s.d. of birth weight for mothers who smoke. Do the same for mothers who don't smoke.
[f] Low birth weight (LBW) is defined to be no more than 88 ounces. Construct a new factor that indicates whether or not a baby has LBW. Create a 2x2 frequency table that gives total number of babies in each combination of categories for LBW and Smoker. Use this to test the null hypothesis of independence between LBW and Smoker at the 5% level of significance.
Use the data in
[a] There are 4 combinations of species and sex (B-M, B-F, O-M, O-F) for the crabs in this data. Construct separate 90% confidence intervals for mean FL for each of these groups.
[b] Construct separate 90% confidence intervals for the s.d. of FL for each of these groups.
[c] Construct a plot of FL versus CL using different colors for the two species and different plot symbols for Male and Female. Include a legend in the plot that shows which colors go with which species and which symbol goes with which sex.
[d] Obtain separate correlation coefficients between FL and CL for each of the 4 combinations of species and sex. Compare these correlations to the overall correlation between FL and CL using all crabs. Interpret these correlation coefficients.
Suppose that scores on the quantitative SAT exam among students in Texas public universities who are taking Calculus I have approximately a normal distribution with mean 580 and s.d. 80.
[a] What proportion of such students scored above 720?
[b] What are the quartiles of these scores?
[c] Suppose there are 35 students in a particular section of Calculus I at UTD and the mean QSAT score for these students is 634 with a s.d. of 94. Treat this class as a random sample of students at UTD who take this course and construct a 95% confidence interval for the mean QSAT. Is the mean QSAT score of all students who take this course at UTD significantly different from the mean for all such students in Texas? Use 5% level of significance.