Question

Lena is a college basketball player who has made 75\%75%75, percent of the free-throws she has attempted in her career. She decided to practice a new technique for shooting her free-throws. Lena was curious if this new technique produced significantly better or worse results. She tried the new technique and made 70\%70%70, percent of 505050 attempts. Here's Lena's alternative hypothesis: H_\text{a}:H a ​ :H, start subscript, start text, a, end text, end subscript, colon The proportion of attempts made using this new technique is... What is an appropriate way for Lena to finish her alternative hypothesis?

Answer 1

The alternate hypothesis statement is, p ≠ 0.75.

Explanation:

Success rate for Lena at free throws in a basketball game is, p = 0.75.

She decided to practice a new technique for shooting her free-throws.

Lena attempted n = 50 free throws. Of these 50 free throws her success rate was,
`\hat p=0.70`.

To test whether the new technique produced significantly better or worse results she should use one-proportion z-test.

The hypothesis can be defined as:

H₀: The proportion of attempts made using this new technique is 75%, i.e. p = 0.75.

Hₐ: The proportion of attempts made using this new technique is different from 75%, i.e. p ≠ 0.75.

The alternative hypothesis indicates that the test is two-tailed.

This is because Lena is not sure if the new technique increases her success rate or decreases it.

Thus, the alternate hypothesis statement is, p ≠ 0.75.