Question

For the following situations, develop the appropriate Ho and Ha and state what the consequences would be for Type 1 and Type 2 errors.

a. A company that manufactures one-half inch bolts selects a random sample of bolts to determine if the diameter of the bolts differs significantly from the required one-half inch.

b. A company that manufactures safety flares randomly selects 100 flares to determine if the flares last at least three hours on average.

c. a consumer group believes that a new sports coupe gets significantly fewer miles to the gallon than advertised on the sales sticker. To confirm this belief, they randomly select several of the new coupes and measure the miles per gallon.

Answer 1

Answer:-

Given that:-

For the following situations, develop the appropriate Ho and Ha and state what the consequences would be for Type 1 and Type 2 errors.

Type I error ( reject Ho | Ho is true ) and

Type II error ( fail to reject Ho | is true )

a. A company that manufactures one-half inch bolts selects a random sample of bolts to determine if the diameter of the bolts differs significantly from the required one-half inch.?

Ho : Length of bolt is one half inch.

: Length of bolt is not equal to one half inch.

Type I error:

We conclude that length of bolt is not equal to one half inch but actual length is one half inch.

Type II error:

We conclude that length of bolt is equal to one half inch but actual length is not equal to one half inch.

b. A company that manufactures safety flares randomly selects 100 flares to determine if the flares last at least three hours on average.?

Type I error:

We conclude that safety flares last on an average less than three hours but actual average safety time of flares is at least three hours.

Type II error:

We conclude that average safety time of flares is at least three hours but actual average safety time is less than three hours.
c. a consumer group believes that a new sports coupe gets significantly fewer miles to the gallon than advertised on the sales sticker. To confirm this belief, they randomly select several of the new coupes and measure the miles per gallon.?

New sport coupe get fewer miles to the gallon that advertised on sales sticker

New sport coupe get fewer miles to gallon that advertised on sales sticker.

We conclude that the new sport coupe get fewer miles to gallon that advertised on sales sticker but actually it give at least miles to gallon.

Type II error:

We conclude that new sport coupe get at least miles to gallon that advertised on sales sticker but actually it gives fewer miles to gallon.