A study was conducted investigating the long-term prognosis of children who have suffered an acute episode of bacterial meningitis, an inflammation of the membranes enclosing the brain and spinal cord.
Listed below are the times to the onset of seizure for 13 children who took part in the study. In months, the measurements are:
0.10 0.25 0.50 4 12 12 24 24 31 36 42 55 96
Find the following numerical summary measures of the data:
Mean
Median
Mode
Range
Interquartile Range
Standard Deviation
How many standard deviations away from the mean is a child whose time to the onset of seizure was 50 months? (Note: for the purpose of this problem, assume that the population standard deviation is the same as the sample standard deviation.)
What proportion of children have an onset to seizure time of 50 or more months?
What proportion of children have an onset to seizure time between the mean and 50 months?
Calculate a 95% confidence interval around the mean assuming that the data are normally distributed with a known population variance of 20
Calculate a 95% confidence interval around the mean assuming that the data are normally distributed with an unknown population variance.
Calculate a 99% confidence interval around the mean assuming that the data are normally distributed with an unknown population variance.
Find the median daily caloric intake for both the bulimic adolescents and the healthy ones.
Compute the IQR for each group.
Construct box-and-whisker plots for each group.
Describe the shape of the observed distribution for each group. Do you think that the sampled data come from a population with a normal distribution? Why or why not?
Describe the qualitative differences between the two groups based on the box-and-whisker plots. (For example, which average is higher? Which group has more variability? Are there outlying values in either group?)
Find the mean and median concentrations of nicotine.
Produce a histogram of the nicotine measurements. Describe the shape of the observed distribution. Do you think that the sampled data come from a population with a normal distribution? Why or why not?
Which number do you think provides the best measure of central tendency for these concentrations, the mean or the median? Why?
Create frequency tables in SPSS of all categorical tables. Attach the output file (can be all one file).
Create a cross-tabulation table of toxemia diagnosis for mother and germinal matrix hemorrhage, including the expected frequencies and column percentages.
Calculate the 90% confidence interval for 𝜇 based on the data collected by the 1st
Calculate the 90% confidence interval for 𝜇 based on the data collected by the 2nd
Interpret the confidence intervals.
Compare the two confidence intervals. Give some possible reasons why they are different.
A library wants to determine the effectiveness of their summer literacy program among low-income children. Because surveying the large numbers of students in the program would require too many resources the library staff interviews 30 randomly chosen children among the low-income program attendees. The 30 sampled children are given a reading test before and after the program.
Describe the population of this study.
The difference in the reading test scores (after – before) has mean = 10 and SD = 4. Assuming the score differences are normally distributed, what percent of the children showed any improvement (difference > 0) in reading ability?
What percent of children improved by more than 15 points?
What is the probability that an outcome z is < -2.05?
What is the probability that an outcome z is > 1.82?
What is the probability that an outcome z is > -1.82?
What is the probability that an outcome z is between –2.28 and 1.92?
What value of z cuts off the upper 30% of the standard normal distribution?
What value of z cuts off the lower 8% of the standard normal distribution?