Suppose we are conducting a hypothesis test with the following hypotheses:H0: p = 0.3H1: p < 0.3Furthermore suppose we take 20 samples and get 3 successes,calculate the p-value correct to 4dp.
Question
Suppose we are conducting a hypothesis test with the following hypotheses:H0: p = 0.3H1: p < 0.3Furthermore suppose we take 20 samples and get 3 successes,calculate the p-value correct to 4dp.
Solution
Sorry, there seems to be a misunderstanding. I'll continue with the calculation of the p-value.
Step 1: Identify a test statistic. Since we are dealing with proportions, we can use the z-test. The test statistic is calculated as follows:
z = (p̂ - p0) / sqrt((p0 * (1 - p0)) / n)
where p̂ is the sample proportion, p0 is the proportion in the null hypothesis, and n is the sample size.
Step 2: Calculate the test statistic. In this case, p̂ = 3/20 = 0.15, p0 = 0.3, and n = 20.
z = (0.15 - 0.3) / sqrt((0.3 * (1 - 0.3)) / 20) = -1.8257
Step 3: Find the p-value. The p-value is the probability of observing a test statistic as extreme as the one calculated (or more extreme) under the null hypothesis. Since this is a one-tailed test (H1: p < 0.3), we want the probability that Z is less than or equal to -1.8257.
Using a standard normal distribution table or a calculator, we find that the p-value is 0.0339 (to 4 decimal places).
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