Question

A local chess club claims that the length of time to play a game has a

standard deviationstandard deviation

of

14 minutes or more14 minutes or more.

Write sentences describing type I and type II errors for a hypothesis test of this claim.

A type I error will occur if the actual

standard deviationstandard deviation

of the length of time to play a game is

▼

equal to

less than or equal to

less than

greater than or equal to

not equal to

greater than

1414

​minutes, but you

▼

reject

fail to reject

the null​ hypothesis,

▼

Upper H 0 : sigma equals 14H0: σ=14

Upper H 0 : sigma greater than 14H0: σ>14

Upper H 0 : sigma not equals 14H0: σ≠14

Upper H 0 : sigma less than 14H0: σ<14

Upper H 0 : sigma greater than or equals 14H0: σ≥14

Upper H 0 : sigma less than or equals 14H0: σ≤14

.A type II error will occur if the actual

standard deviationstandard deviation

of the length of time to play a game is

▼

less than or equal to

equal to

not equal to

greater than

less than

greater than or equal to

1414

​minutes, but you

▼

reject

fail to reject

the null​ hypothesis,

▼

Upper H 0 : sigma less than 14H0: σ<14

Upper H 0 : sigma greater than 14H0: σ>14

Upper H 0 : sigma equals 14H0: σ=14

Upper H 0 : sigma not equals 14H0: σ≠14

Upper H 0 : sigma less than or equals 14H0: σ≤14

Upper H 0 : sigma greater than or equals 14H0: σ≥14

.

Answer 1

Type I error:

A type I error will occur if the actual standard deviation of the length of time to play a game is greater than or equal to 14

​minutes, but you reject the null​ hypothesis, H0: σ≥14

Type II error:

A type II error will occur if the actual standard deviation of the length of time to play a game is less than 14 ​minutes, but you fail to reject the null​ hypothesis, H0: σ≥14