To solve this problem, we will go through the following steps:
### Step 1: Understand the given information
- Test statistic: [tex]\( z = -1.08 \)[/tex]
- Level of significance: [tex]\( \alpha = 0.05 \)[/tex]
### Step 2: Calculate the p-value for the left-tailed test
The p-value for a left-tailed test can be found by determining the cumulative probability associated with the given z-score. In this case, the p-value corresponding to [tex]\( z = -1.08 \)[/tex] is approximately [tex]\( 0.1401 \)[/tex].
### Step 3: Compare the p-value with the level of significance
We compare the p-value to the level of significance to decide whether to reject the null hypothesis [tex]\( H_0 \)[/tex].
- If [tex]\( \text{p-value} \leq \alpha \)[/tex], we reject the null hypothesis.
- If [tex]\( \text{p-value} > \alpha \)[/tex], we do not reject the null hypothesis.
Given:
- p-value [tex]\( \approx 0.1401 \)[/tex]
- [tex]\( \alpha = 0.05 \)[/tex]
Since [tex]\( 0.1401 > 0.05 \)[/tex], we do not reject the null hypothesis [tex]\( H_0 \)[/tex].
### Conclusion
The p-value for the left-tailed hypothesis test with a test statistic of [tex]\( z = -1.08 \)[/tex] is approximately [tex]\( 0.1401 \)[/tex]. Since this p-value is greater than the level of significance [tex]\( \alpha = 0.05 \)[/tex], we do not reject the null hypothesis [tex]\( H_0 \)[/tex].
