Final answer:
Without additional context on the alternative hypothesis, we cannot definitively determine if the test is two-tailed, left-tailed, or right-tailed. The test statistic z=1.45 suggests a right-tailed test, and with a critical z-value of α = 0.05 being 1.645, it hints that we would fail to reject the null hypothesis as the test statistic is less than the critical value.
Step-by-step explanation:
Identification of Hypothesis Test Type and Decision-Making
When determining the type of hypothesis test, we look at the alternative hypothesis (Ha). Since the claim states p = 0.688, but the type of inequality is not specified, we need additional information to determine if the test is two-tailed, left-tailed, or right-tailed. However, given that the test statistic z = 1.45 is a positive value, it suggests a right-tailed test if the alternative hypothesis implies p > 0.688. Without explicit information on Ha, we cannot definitively determine the type of test.
For the P-value, we need to calculate the area to the right of z = 1.45 in a standard normal distribution; unfortunately, without a standard z-table or calculator at hand, we cannot provide the exact P-value. To make conclusions based on a significance level of α = 0.05, we would compare the P-value to α. If the P-value is less than α, we would reject the null hypothesis (H0); if it's greater, we would fail to reject H0. Decisions on the null hypothesis typically depend on these comparisons.
The critical z-value of α = 0.05 in a right-tailed test is approximately 1.645. Since 1.45 is less than 1.645, this suggests that we should fail to reject H0 as the test statistic does not fall into the critical region. However, without a specific P-value, this conclusion is theoretical and should be calculated precisely given the appropriate tables or software.