Question

Suppose you heard from a friend that only 75% of people pass Math 1044. In disbelief, you poll 50 randomly selected Math 1044 students and find that 43 of them passed. Answer the following questions with a significance threshold of α = 0.05. You may assume the success-failure conditions hold.

(a) What is the null hypothesis, H0, for this experiment?

(b) What are two valid alternative hypotheses, Ha for this experiment?

(c) Compute the p-value for this experiment using a one-tailed test.

(d) Would we accept or reject H0 using the one-tailed p-value? Justify.

(e) Compute the p-value for this experiment using a two-tailed test.

(f) Would we accept or reject H0 using the two-tailed p-value? Justify.

Answer 1

Answer a)

The null hypothesis, H0, for this experiment is: p = 0.75

Answer b)

The alternative hypothesis Ha for this experiment is p ≠ 0.75 (For two tailed test)

Another alternative hypothesis Ha for this experiment can be p > 0.75 ( For one tailed test)

Answer c)

P-value corresponding to z = 1.796 for a one-tailed test is obtained using p-value calculator. Screenshot below:

P-value = 0.0362

Answer d)

Since p-value = 0.0362 < α = 0.05, we reject H0.

Answer e)

P-value corresponding to z = 1.796 for a two-tailed test is obtained using p-value calculator. Screenshot below:

P-value = 0.0725

Answer f)

Since p-value = 0.0725 > α = 0.05, we accept H0.