Math 58B - Introduction to Biostatistics
Spring 2014
Jo Hardin
Lab Assignment 3
Lab Goals:
1.
To understand what a z-score means.
2.
3.
To learn how to calculate z-scores.
To learn how to calculate probabilities from z-scores using a normal model (in
comparison to the corresponding probabilities found using a binomial model).
In class
During the lab, go through sections (a) through (k) of Investigation 1.8. Make sure you
know how to compute probabilities using both the normal and binomial distributions
(iscambinomprob [page 22], iscamnormprob [page 59], and xpnorm [mosaic]).
Note 1: if you can't remember what an ISCAM function does, pass it the argument "?". Also,
remember to look at the back of each chapter for R summaries.
load(url("http://www.rossmanchance.com/iscam2/ISCAM.RData"))
iscamnormprob("?")
## Error in iscamnormprob("?"): iscamnormprob(xval, mean, sd, direction,
label, xval2)
## This function calculates tail probability for the normal distribution.
## Direction is a String for finding the probability above ("above") or
below ("below") the inputted value
## If "outside" or "between " are specified, a second observation needs to
be given at the end.
##
It is highly recommended that you indicate a label for the horizontal
axis, with the quotation marks (e.g., "sample proportions")
Note 2: We are skipping the continuity correction [pages 65-66] and the adjusted Wald
intervals in Investigation 1.11.
To turn in
1.
Do you think the normal approximation works well in this investigation to compute
probabilities? Explain.
2.
Give one reason we might prefer binomial probabilities in this setting.
3.
Give one reason we might prefer normal probabilities in this setting.
4.
Consider the investigation. Assume a sample size of 329 sessions. Additionally,
assume that the null hypothesized value for 𝜋 = .25 is true. For each probability
below [parts (a) - (e)] turn in 5 things:
(i) The probability statement of interest (e.g., P(47 < X < 50)). Assume X counts the
number of "hits" in 329 sessions. (no technology)
(ii) A sketch (by hand) of a normal curve with the appropriate area shaded in. (no
technology). Your sketch should include a center, a st dev, a z-score, shading, and a
number (area) associated with how much area is shaded in.
(iii) The appropriate normal probability (a number). (iscamnormprob, page 59 or
xpnorm, mosaic)
(iv) The appropriate binomial probability (a number). (iscambinomprob, page 22)
(v) The relevant z-score(s) (a number or two) (calculator)
(a) The probability of 80 or more hits.
(b) The probability of 100 or fewer hits.
(c ) The probability of exactly 106 hits.
(c) The probability of between 85 and 100 hits.
(d) The probability of fewer than 75 or more than 90 hits.
5. Practice Problem 1.13B (no technology)