To solve the problem, we will follow these steps:
1. Understand the given information:
- The test statistic for the left-tailed test is [tex]\( z = -1.83 \)[/tex].
- The significance level (alpha) is [tex]\( 0.05 \)[/tex].
2. Calculate the P-value:
- The P-value corresponds to the cumulative probability of obtaining a value less than or equal to the test statistic in the standard normal distribution. Given [tex]\( z = -1.83 \)[/tex], we find the P-value as approximately [tex]\( 0.0336 \)[/tex].
3. Decision Rule:
- Compare the P-value with the significance level.
- If the P-value [tex]\( < 0.05 \)[/tex], we reject the null hypothesis.
- If the P-value [tex]\( \geq 0.05 \)[/tex], we fail to reject the null hypothesis.
4. Make the conclusion:
- Since the P-value [tex]\( 0.0336 \)[/tex] is less than the significance level [tex]\( 0.05 \)[/tex], we reject the null hypothesis.
Therefore, the correct interpretation is:
- With a test statistic of [tex]\( z = -1.83 \)[/tex] and a significance level of [tex]\( 0.05 \)[/tex], the P-value is approximately [tex]\( 0.0336 \)[/tex].
- Since [tex]\( 0.0336 \)[/tex] is less than [tex]\( 0.05 \)[/tex], we reject the null hypothesis.
Thus, the answer is:
- [tex]\( 0.0336 \)[/tex]; reject the null hypothesis.
This matches the choice [tex]\( 0.0336 \)[/tex]; reject the null hypothesis.
