t Procedures
Worksheet 22
1. A rule of thumb for maximum heart rate is 220 − age beats per minute where age is measured in years.
Thus, the mean maximum heart rate for 22 year-olds would be 198 beats per second. You want to test
this.
(a) Give an appropriate hypothesis for this rule of thumb using the independent measurements of
healthy 22 year olds. Define any populations parameters in your hypothesis.
(b) Here are the data for the maximum heart rate on ten 22 year-olds.
202
191
195
196
198
196
199
190
191
200
Give the mean and variance for these data.
(c) Give the value of the test statistic for this hypothesis.
(d) Do you reject the hypotheses? Explain your answer.
(e) Using the standard deviation from the data, how many observations are necessary to detect a
heart rate change of 3 beats per minute with 80% power for a test at the 5% significance level.
2. NFL released the results of an investigation of a 2014 playoff game between the New England Patriots
and the Indianapolis Colts. Their question was: Did the Patriots intentionally deflated footballs below
league standards and thus were lower than their opponent? Below are summaries of football pressure
in pounds per square inch for one set of measurements.
team
New England Patriots
Indianapolis Colts
# balls
11
4
mean
11.11
12.62
standard
deviation
0.12
0.40
(a) State a hypothesis appropriate to this situation. Define any a parameter appearing in your
statement.
(b) Describe the testing procedure – one-sample, two-sample, or matched pair. Explain your answer.
(c) Give a 99% confidence interval for the mean difference in the mean pressure in the balls for the
two teams. Use 13 degrees of freedom to compute the interval.
(d) Do you reject the null hypothesis at the 0.005 significance level? Explain your answer.
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