Question

A local chess club claims that the length of time to play a game has a standard deviation of less than 11 minutes. Write sentences describing type l and type ll errors for a hypothesis test of this claim. A type I error will occur if the actual standard deviation of the length of time to play a game is hypothesis, A type Il error will occur if the actual standard deviation of the length of time to play a game is hypothesis, the null 11 minutes, but you 11 minutes, but you the null

Answer 1

Solution

Definitions

Type 1 error: If the null hypothesis(H0) is TRUE and we reject this null hypothesis , then the eroor is called as Type 1 error.

Type 2 error: If the null hypothesis is FALSE and ew fail to reject the this null hypothesis , then it is Type 2 error>

Given claim to be tested is

"Standard deviation is less than 11 minutes"

So, hypothesis can be written as

H0:      11 (null hypothesis)

σ>

H1:   $\sigma<$ 11 (alternative )

Type 1 error will occur if the actual standard deviation of the length of time to play is GREATER OR EQUAL TO 11 minutes and you REJECT the null hypothesis     11

σ>

Type 2 error will occur if the actual standard deviation of the length of time to play is LESS THAN 11 minutes and you FAIL TO REJECT the null hypothesis      11

σ>