# 4.26 In a lottery game, three winning numbers are chosen uniformly at random from (1, ,100), samp...

4.26 In a lottery game, three winning numbers are chosen uniformly at random from (1, ,100), sampling without replacement. Lottery tickets cost \$1 and allow a player to pick three numbers. If a player matches the three winning numbers they win the jackpot prize of \$1,000. For matching exactly two numbers, they win \$15. For matching exactly one number they win \$3
d) Hoppe shows that the probability that a single parlayed ticket will ulti- mately win the jackpot is approximately p/(1), where p is the probabil ity that a single ticket wins the jackpot, and m is the mean of the offspring distribution of the associated branching process. Find this probability and show that the parlaying strategy increases the probability that a ticket will ultimately win the jackpot by slightly over 40%.

Two ways to increase the statistical power of an experiment
Each increases the probability of determining a real effect of the independent variable:
Increase the sample size: Power is higher with one-tailed test rather than with a two-tailed test. A one-tailed test raises the significance level. Larger sample size gives a narrower sampling distribution, i.e., less overlap in the two sampling distributions for null hypothesis and alternative hypothesis.
Larger the sample size, the higher the power.

smaller variance yields higher power. Power is higher when the standard deviation is smaller than when it is large. Reasearcher can control the standard deviation by sapling from a homogeneous population of subjects, by reducing random measurement error and by making sure the experimental procedures are annliart rnnsictontly

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