Question

1. Below are descriptions of questions that might be researched. For each item, state the relevant null and alternative hypotheses both in English and in the form of a probability statement.
   1. A new therapy is being tested for reducing nausea in patients undergoing treatment for cancer. Under conventional therapies, 60% of patients suffer from nause In the experiment, a random sample of 18 patients undergoing cancer treatment is given the new anti-nausea therapy.
   2. A school system has a problem with turn-over among their new teachers, losing 30% of its new teachers within 2 years of their hiring. The superintendent institutes a program of mentoring for new teachers that he hopes will improve retention. After the first 2 years of the program, he evaluates whether it is working by recording what happened with the 16 teachers hired at the start of the mentoring program.
   3. A basketball player claims that she can shoot at least 85% from the foul line. Her coach tests her boast by having her take 20 foul shots while he records the number of made baskets.

Answer 1

Answer:

Part a

The required null and alternative hypotheses for the given scenario are given as below:

Null hypothesis: H₀: A new therapy do not reduces nausea in patients undergoing treatment for cancer.

Alternative hypothesis: A new therapy reduces nausea in patients undergoing treatment for cancer.

H₀: p = 0.60 versus H_a: p < 0.60

Part b

The required null and alternative hypotheses for the given scenario are given as below:

Null hypothesis: H₀: A school system loses 30% of its new teachers within 2 years of hiring.

Alternative hypothesis: A school system loses less than 30% of its new teachers within 2 years of hiring.

H₀: p = 0.30 versus H_a: p < 0.30

Part c

The required null and alternative hypotheses for the given scenario are given as below:

Null hypothesis: H₀: A Basketball player shoot at least 85% from the foul line.

Alternative hypothesis: A Basketball player shoots less than 85% from the foul line.

H₀: p ≤ 0.85 versus H_a: p < 0.85