Question

Suppose that we want to test H0 : p = 0.5 vs Ha : p > 0.5 where the parameter p is the probability of occurrence of some event, e.g., a coin falling heads. Let us use X, the number of successes on n = 4 trials, as the test statistic. (a) If when the data are gathered, x = 2. Find the P-value. (b) If Ha : p ? 0.5, what is the P-value for x = 2?

          Suppose that we want to test
H0 : p = 0.5 vs Ha : p > 0.5
where the parameter p is the probability of occurrence of some event, e.g., a coin falling heads. Let us use X, the number of successes on n = 4 trials, as the test statistic.
(a) If when the data are gathered, x = 2. Find the P-value.
(b) If Ha : p ? 0.5, what is the P-value for x = 2?

Suppose that we want to test
H0 : p = 0.5 vs Ha : p > 0.5
where the parameter p is the probability of occurrence of some event, e.g., a coin falling heads. Let us use X, the number of successes on n = 4 trials, as the test statistic.
(a) If when the data are gathered, x = 2. Find the P-value.
(b) If Ha : p ? 0.5, what is the P-value for x = 2?

Added by Nathan R.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Adi S

07/03/2023

Step 1

Since we are dealing with a proportion, we can use the binomial distribution. Under the null hypothesis, the test statistic X follows a binomial distribution with parameters n and p = 0.5: $$X \sim B(n, 0.5)$$ (a) Show more…

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Suppose that we want to test Ho : p = 0.5 vs Ha : p > 0.5 where the parameter p is the probability of occurrence of some event, e.g., a coin falling heads. Let us use X, the number of successes on n = 4 trials, as the test statistic. (a) If when the data are gathered, x = 2. Find the P-value. (b) If Ha : p ≠ 0.5, what is the P-value for x = 2?