Suppose we are testing the null hypothesis H0: ì = 20 and the alternative Ha: ì 20, for a normal population with ó = 5. A random sample of 25 observations are drawn from the population, and we find the sample mean of these observations is = 17.6. The P-value is closest to?
A. 0.0668.
B. 0.0082.
C. 0.0164.
D. 0.1336.
Two tailed. = 0.0164
Left tailed = 0.0082
To find the P-value, we need to perform a hypothesis test using the sample mean and the population mean. Given that the population standard deviation (σ) is 5, the sample size (n) is 25, the sample mean (x̄) is 17.6, and the null hypothesis (H0) states that the population mean (μ) is equal to 20, we can calculate the test statistic Z using the formula:
Z = (x̄ - μ) / (σ / √n)
Substituting the given values:
Z = (17.6 - 20) / (5 / √25) = -2.4
Next, we need to find the corresponding area under the standard normal distribution curve to determine the P-value. Since the alternative hypothesis (Ha) states that μ ≠ 20 (two-tailed test), we need to find the area in both tails of the distribution.
Using a standard normal distribution table or a calculator, we find the area in the left tail for Z = -2.4 is approximately 0.0082. Since it's a two-tailed test, we multiply this value by 2:
P-value = 0.0082 * 2 = 0.0164
Therefore, the P-value is closest to C. 0.0164.