A friend is interested in beco

To test whether getting more sleep might help in becoming abetter chess player, two identical groups of chess player can beformed using random sampling taking an appropriate sample size (sayn1 and n2) from his school of the same class standard.

One group of players are made to sleep for 10 hours and theother group of players are made to sleep for 6 hours. The chessgame can be conducted the next day and the match won or lost can benoted.

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

Let the proportion of players getting 10 hours of sleep andwinning the chess game be p1 and the proportion of players getting6 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 thegame.

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

P1 = P2

Alternative hypothesis : proportion of players winning in 10hours sleep group is greater than proportion of players winning in6 hours sleep group.

P1> P2

Now, these proportion can be tested using the z test using theformula –

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

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