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Biostats SDS 328M Homework 4     Part 1 – Hand work (all work must be done by hand)

Statistics

Biostats SDS 328M Homework 4

Part 1 – Hand work (all work must be done by hand).

Round all answers to at least 3 decimal places and assume that α=0.05 unless otherwise noted.

1. In a study of nerve cells, researchers measured the timing of spontaneous electrical discharges in a single organism. The interspike-time intervals were approximately normally distributed with a mean of 15.28 ms and a standard deviation of 0.39 ms.  Suppose you measured a random sample of n = 5 interspike-time intervals from this population.

a. What is the probability that all five times in your sample are between 15.00 and

15.50 ms? (3pt)

1. What is the probability that the sample mean time for your sample is between

15.00 and 15.50 ms? (3pt)

1. Comparing the probabilities you calculated in parts (a) and (b), which is larger? Despite what the mean and standard deviation of the population are, explain why this will always be the case. (2pt)

1. Suppose you conducted a hypothesis test to determine if caffeine intake increases anxiety.

1. State the appropriate null and alternative hypotheses for this study. (2pt)

1. Explain what a Type-I error would mean in context. (1pt)

1. Explain what a Type-II error would mean in context. (1pt)

1. If your test resulted in a p-value of 0.03, what would be your conclusion in the context of the problem? (1pt)

Part 2 – R work (must be done in R)

Copy and paste your R code and output into a word document to submit to Canvas.

Follow these instructions to import the necessary dataset:

x Before opening the dataset needed for this problem, you’ll need to call the “car” package (if you didn’t install this package for HW3, go back to that assignment for directions on how to install it).  Run the following line of code:

> library(car)

x Now you can import the “Robey” dataset and use it to answer the question below.  Name the data frame with your UT EID:

> my_eid <- Robey

3. The Robey dataset contains fertility rates from a sample of countries.  The row.names variable lists the country name and region gives the region each country is in.  The tfr variable is the total fertility rate (average number of children per woman), and contraceptors is the percent of married women of childbearing age who use contraception.

1. Find the number of countries from each region in the dataset. (1pt)

1. Create a display for the total fertility rate and describe the distribution with the appropriate statistics. (3pt)

1. How is total fertility rate related to percent contraceptors?  Create an appropriate graph for this relationship and summarize what the graph shows in 1 or 2 short sentences. (3pt)

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