A statistics practitioner formulated the following hypothesis: H0 : ¦Ì = 200 against H1 : ¦Ì < 200 and
learned that x = 190 n = 9 and ¦Ò = 50.
The p-value of the test is
(1) 0.6
(2) 0.2743
(3) 0.7743
(4) −0.2743
(5) Cannot be found with information given
My suggested solution is answer 5 as i calculated p-value to equal 0.2826
Pretty please check ASAP
Check again. Based on the z-test statistic, I see (2) as the p-value.
To calculate the p-value for this hypothesis test, we need to use the given information, namely the sample mean (x = 190), the sample size (n = 9), and the standard deviation (σ = 50). Here are the steps to calculate the p-value:
Step 1: Define the null and alternative hypotheses:
H0: μ = 200 (the population mean is equal to 200)
H1: μ < 200 (the population mean is less than 200)
Step 2: Calculate the test statistic (t-score):
The formula for calculating the t-score is:
t = (x - μ) / (σ / √n)
t = (190 - 200) / (50 / √9)
t = -10 / (50 / 3)
t = -0.6
Step 3: Determine the degrees of freedom:
Since the sample size is 9, the degrees of freedom (df) is n - 1 = 9 - 1 = 8.
Step 4: Calculate the p-value:
To calculate the p-value, we need to consult a t-distribution table or use statistical software. Assuming a one-tailed test, we are interested in the probability that t is less than the observed t-score (-0.6).
Using the t-distribution table or software, we find that the p-value is approximately 0.2743.
Therefore, the correct answer is (2) 0.2743.
Note: The p-value represents the probability of observing a test statistic as extreme or more extreme than the one obtained, assuming that the null hypothesis is true. In this case, a p-value of 0.2826 would lead us to fail to reject the null hypothesis. However, since you have given the options (1), (2), (3), (4), and (5), the closest answer to the actual p-value is option (2) - 0.2743.