Questions: Question 7 You are performing a two-tailed test with test statistic z=-1.68, find the p-value to 4 decimal places

Solution Steps

To find the p-value for the two-tailed test with the test statistic \( z = -1.68 \), we first calculate the probability of the sample mean falling between the z-scores of \( -1.68 \) and \( 1.68 \):

\[ P = \Phi(Z_{end}) - \Phi(Z_{start}) = \Phi(1.68) - \Phi(-1.68) = 0.907 \]

The p-value for a two-tailed test is calculated as twice the probability of observing a value as extreme as the test statistic in either tail of the distribution:

\[ \text{P-value} = 2 \times (1 - P) = 2 \times (1 - 0.907) = 2 \times 0.093 = 0.1860 \]

Final Answer