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Suppose the null hypothesis, H0, is: a sporting goods store claims that at least 70% of its customers do not shop at any other sporting goods stores. What is the Type I error in this scenario?

(A) The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.
(B) The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.
(C) The sporting goods store thinks that less than 70% of its customers do not shop at any other sporting goods stores when, in fact, at least 70% of its customers do not shop at any other sporting goods stores.
(D) The sporting goods store thinks that at least 70% of its customers do not shop at any other sporting goods stores when, in fact, less than 70% of its customers do not shop at any other sporting goods stores.

Respuesta :

Answer:

Type I error:

Rejecting the null hypothesis when it is true.

Step-by-step explanation:

We are given the following in the question:

Claim:

At least 70% of its customers do not shop at any other sporting goods stores.

First, we design the null and the alternate hypothesis  

[tex]H_{0}: p \leq 0.7\\H_A: p > 0.7[/tex]

Type I  error:

  • It is the error when we rejects the null hypothesis given it is true.
  • It is also known as false positive.

Thus, for this scenario type I error would be rejecting the null hypothesis that the proportion of customers that do not shop at any other sporting goods stores is less than 0.7 provided it is true.

Interpretation:

Thus, it is the probability that the sporting good store thinks that atleast 70% of its customers do not shop at any other sporting goods stores but actually less than 70% of customers do not shop from other sporting goods stores.

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