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From previous experience, the owner of an apple orchard knows that the mean weight of Gala apples is 140 grams. There has been more precipitation than usual this year. The owner believes the weights of the apples will be heavier than usual and therefore the crop will be more profitable. This will allow the owner to expand the orchard. The owner takes a random sample of 30 apples and records their mean weight. What is the consequence of a Type I error in this situation?

The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually greater than 140 grams.
The owner believes the crop will not be more profitable and does not expand the orchard when the true mean weight of the apples is actually greater than 140 grams.
The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.
The owner believes the crop will not be more profitable and does not expand the orchard when the true mean weight of the apples is actually not greater than 140 grams.

Respuesta :

Answer:

C, The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.

Step-by-step explanation:

Using error concepts, it is found that the consequence of a Type I error in this situation in this situation is given by:

The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.

What are the hypotheses test?

At the null hypotheses, it is tested if the weights are not heavier, that is:

[tex]H_0: \mu = 140[/tex]

At the alternative hypotheses, it is tested if they are heavier, that is:

[tex]H_1: \mu > 140[/tex]

A Type I error is the rejection of a true null hypothesis, that is, concluding that the weights are heavier and more profitable when they are not. Hence the correct option is:

The owner believes the crop will be more profitable and expands the orchard when the true mean weight of the apples is actually not greater than 140 grams.

More can be learned about Type I and Type II errors at https://brainly.com/question/25225353

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