A statistics practitioner formulated the following hypothesis: H0 : ì = 200 against H1 : ì < 200 and
learned that x = 190 n = 9 and ó = 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
To find the p-value for this hypothesis test, we need to calculate the test statistic and compare it to the appropriate distribution.
In this case, we are given the following information:
- The null hypothesis, H0: ì = 200
- The alternative hypothesis, H1: ì < 200
- Sample mean, x = 190
- Sample size, n = 9
- Population standard deviation, σ = 50
First, we need to calculate the test statistic, which is the z-score in this case. The formula for calculating the z-score is:
z = (x - ì) / (σ / sqrt(n))
Plugging in the values we have:
z = (190 - 200) / (50 / sqrt(9))
z = -10 / (50 / 3)
z = -0.6
Next, we need to find the p-value associated with this test statistic. The p-value is the probability of obtaining a test statistic as extreme or more extreme than the observed value, assuming the null hypothesis is true.
Since the alternative hypothesis is ì < 200, we are interested in the left-tail of the standard normal distribution. We can use a standard normal distribution table, calculator, or software to find the probability associated with the z-score of -0.6.
Looking up a z-score of -0.6, we find that the corresponding p-value is approximately 0.2743.
Therefore, the correct answer is (2) 0.2743.