Question

A friend is interested in becoming a better chess player. He thinks that perhaps getting more sleep might help him and wonders whether people play better after getting 10 hours of sleep or after getting 6 hours of sleep. How should he design a study to test this question and how should he analyze his data?

Answer 1

To test whether getting more sleep might help in becoming a better chess player, two identical groups of chess player can be formed using random sampling taking an appropriate sample size (say n1 and n2) from his school of the same class standard.

One group of players are made to sleep for 10 hours and the other group of players are made to sleep for 6 hours. The chess game can be conducted the next day and the match won or lost can be noted.

Then, the proportion of players winning the chess game of both the groups can be calculated from the sample.

Let the proportion of players getting 10 hours of sleep and winning the chess game be p1 and the proportion of players getting 6 hours of sleep and winning the chess game be p2.

Hypothesis can be framed as -

Null hypothesis : There is no effect of sleep on winning the game.

i.e proportion of players winning in 10 hours sleep group is same as the proportion of players winning in 6 hours group.

P1 = P2

Alternative hypothesis : proportion of players winning in 10 hours sleep group is greater than proportion of players winning in 6 hours sleep group.

P1> P2

Now, these proportion can be tested using the z test using the formula -

where, p is the pooled proportion and is equal to number of matches won by players of both groups/ total number of players

The calculated z score can be tested from the critical value at any selected level of significance (i.e 1% or 5%) using rejection region criteria accordingly we can conclude wgethwh to accept or reject the null hypothesis.