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A friend of yours claims that they are a 75% free-throw shooter in basketball. You don't think she is that good and want to test her to gather evidence that she makes less than 75% of her free throws in the long run. You have her shoot 40 free throws and she makes 26 (or 65%) of them. You run your hypothesis test and find a p-value of 0.1150. Which of the following is the best way to state the conclusion? Use a = 0.05.
i. Because the p-value is large, there is strong evidence that your friend is a 65% free-throw shooter in the long run.
ii. Because the p-value is small, there is strong evidence that your friend is a 75% free-throw shooter in the long run.
iii. Because the p-value is small, there is strong evidence that your friend is less than 75% free-throw shooter in the long run.
iv. Because the p-value is large, there is strong evidence that your friend is a 75% free-throw shooter in the long run.
v. Because your p-value is not small enough, there is not strong evidence that your friend is less than 75% free-throw shooter in the long run.

Answer :

According to the hypothesis tested and the p-value given, it is found that the correct option is:

  • v. Because your p-value is not small enough, there is not strong evidence that your friend is less than 75% free-throw shooter in the long run.

What are the hypothesis tested?

  • At the null hypothesis, it is tested if the proportion is of 75%, that is:

[tex]H_0: p = 0.75[/tex]

  • At the alternative hypothesis, it is tested if the proportion is of less than 75%, that is:

[tex]H_1: p < 0.75[/tex]

How a conclusion is reached according to the p-value?

  • If the p-value is greater than the significance value, the null hypothesis is not rejected.
  • If the p-value is less than the significance value, the null hypothesis is rejected.

In this problem:

  • p-value of 0.115.
  • Significance level of 0.05.
  • Hence, not enough evidence to reject the null hypothesis, that is, not strong evidence that your friend is less than 75% free-throw shooter in the long run, hence option v is correct.

A similar problem, involving an hypothesis and a p-value, is given at https://brainly.com/question/16313918

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