Question

In testing H₀: µ = 100 versus H_a: µ ╪ 100 versus using a sample size of 325, the value of the test statistic was found to be 2.16. The p-value (observed level of significance) is best approximated by

0.0154

0.9692

0.4846

0.0308

0.007

Answer 1

Answer 2

To find the p-value, we need to determine the probability of observing a test statistic as extreme or more extreme than the one calculated under the null hypothesis (H0: µ = 100). Since the alternative hypothesis (Ha: µ ≠ 100) is two-tailed, we look for extreme values in both tails of the distribution.

The p-value is the probability of getting a test statistic as extreme or more extreme than the observed value of 2.16. This probability is represented by the shaded area in the tails of the t-distribution.

However, since the p-value is not given for the exact value of 2.16, we can use a statistical table or calculator to approximate it.

For a two-tailed test with a test statistic value of 2.16 and a sample size of 325 (which results in degrees of freedom close to 324), the approximate p-value is around 0.0308.

Therefore, the best approximated p-value from the given options is 0.0308.