The following problems are copied from the chapter 19 exercises from Introduction to Modern Statistics First Edition by Mine Çetinkaya-Rundel and Johanna Hardin (https://openintro-ims.netlify.app/inference-one-mean.html#chp19-exercises)

  1. Statistics vs. parameters: one mean. Each of the following scenarios were set up to assess an average value. For each one, identify, in words: the statistic and the parameter.
  1. Georgianna samples 20 children from a particular city and measures how many years they have each been playing piano.

ANSWER: Average age of 20 piano players in a particular city sample versus the average age of all the children who play piano in a particular city.

  1. Traffic police officers (who are regularly exposed to lead from automobile exhaust) had their lead levels measured in their blood.

ANSWER: average lead level in traffic police officers vs everyone else.

The following is a modified version of problem 5.

  1. Heights of adults. Researchers studying anthropometry collected body measurements, as well as age, weight, height and gender, for 507 physically active individuals. The distribution of heights (measured in centimeters), is displayed below. The data set is part of the openintro package and is called bdims. (Heinz et al. 2003)
bdims %>%
  ggplot(aes(x=hgt)) + 
  geom_histogram(binwidth=2, color="white",fill="steelblue") +
  labs(x="Height (centimeters)") +
  theme_bw()

  1. Calculate the summary statistics for height. (The mosaic package is already loaded in the document.)
favstats(bdims$hgt) %>% round(1)
##    min    Q1 median    Q3   max  mean  sd   n missing
##  147.2 163.8  170.3 177.8 198.1 171.1 9.4 507       0
  1. What statistics would you use to summarize the center and spread of the distribution? Briefly explain your answer.

ANSWER: I would use the mean and standard deviation as the data is roughly normal shaped

  1. Is a person who is 1m 80cm (180 cm) tall considered unusually tall? Explain your answer.

ANSWER: They are taller than Q3 so yes they are taller than 75% of individuals in the sample, however, I would not consider this to be unusually tall as it is still less than the maximum

  1. The researchers take another random sample of physically active individuals. Would you expect the mean and the standard deviation of this new sample to be the same as the ones you calculated above? Explain your reasoning.

ANSWER: Yes, as because the size was sufficiently large, and observations were independent this normal distributions center should match that of the average proportion of physically active individuals.

  1. Would it be appropriate to use a t statistic to calculate a confidence interval or to conduct a hypothesis test?
    Explain your answer.

ANSWER: Yes as the sample size was sufficiently large as the n value was equal and on top of that there was no significant outliers.

Date and time completed: Thu Nov 10 09:28:46 2022