Team 1 - Feb 21 Activity

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Team 1 is:

Todd Swinson, Nick Wilson


What is the data, what test statistic will be computed on this data, what is the null model, and how will this test statistic will be distributed under the null model?

Experiments:

  • Does one pride of lions have a different sex ratio than others?

The data is sex of each lion in a pride.

The test statistic is the ratio of male to female in our data.

The null hypothesis is normal centered on the expected ratio of males to females (say 1:4). This was obtained by measuring the sex ration in 100 different prides. The data fit a normal distribution with mean 0.25.

The test statistic is distributed as a normal distribution under the null hypothesis.


  • Are the odds given for winning a lottery accurate?

The data is the observed outcomes from N tickets.

The test statistic is the number of wins after buying N tickets.

The null hypothesis is distributed as a binomial distribution with p being the given odds of winning, and N being the number of tickets played.

The test statistic is distributed as a binomial distribution with p being the given odds of winning, and N being the number of tickets played.


  • Are GPS coordinates given by a device accurate?

The data is a collection of GPS readings paired with the actual "real" coordinates.

The test statistic is the difference between the GPS reading and the actual location (this is a distance).

The null model is a normal distribution with mean 0 and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \sigma=} the stated accuracy of the device (in meters).

The test statistic is distributed normally under the null hypothesis.



  • Are traffic lights lasting as long as their quoted time to failure?

The data is observing the time to failure of real light bulbs in the wild.

The test statistic is the mean (scaled sum) of the observed times to failure.

The null model is an exponential distribution with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lambda=0.01} , which gives a mean time to failure of 100 hours.

The test statistic is distributed as a Gamma distribution because it is the sum of several exponential distributions.