Question

1.3.10 Recall that one of the authors likes to play the game Minesweeper (Exercise 1.1.8) and in the last 20 games she played she won 12. Use an applet to conduct appropriate simulations in order to calculate the standardized statistic for these data and investigate whether her results provide convincing evidence that her long-run proportion of winning at Minesweeper is higher than 50%?

Report the calculated standardized statistic and use it to state a conclusion about the strength of evidence.

Answer 1

Given that, n = 20 and x = 12

sample proportion = 12/20 = 0.60

The null and alternative hypotheses are,

H_{​​​​​​0} : p = 0.50

H_{​​​​​​a} : p > 0.50

Test statistic is,

Therefore, calculated standardized statistic is, Z = 0.89

p-value= P(Z > 0.89) =1 - P(Z < 0.89) = 1 - 0.8133 = 0.1867

=> p-value = 0.1867

Since, p-value = 0.1867 > 0.05

we fail to reject the null hypothesis.

There is data does not provide convincing evidence that her long-run proportion of winning at Minesweeper is higher than 50%.