Final answer:
- -4. In this case, the test statistic (z) is approximately -2.89.
- - 5. The p-value is less than 0.001. ( Option E)
Step-by-step explanation:
4) To calculate the test statistic (z) and find the p-value, we can follow these steps:
Step 1: State the null and alternative hypotheses.
- - Null hypothesis (H0): The population mean weight is equal to 235 grams. H0: μ = 235
- - Alternative hypothesis (H1): The population mean weight is less than 235 grams. H1: μ < 235
Step 2: Calculate the test statistic (z).
The test statistic (z) can be calculated using the formula:
z = (X - μ) / (σ / √n)
Given that the sample mean (X) is 233.4 grams, the population mean (μ) is 235 grams, the population standard deviation (σ) is 3.5 grams, and the sample size (n) is 40 bags, we can substitute these values into the formula:
z = (233.4 - 235) / (3.5 / √40)
z ≈ -2.89 (rounded to 2 decimal places)
The test statistic (z) is approximately -2.89.
5) Find the p-value.
The p-value represents the probability of obtaining a test statistic as extreme as the observed one, assuming the null hypothesis is true. Since we are conducting a one-tailed test (looking for evidence that the population mean weight is less than 235 grams), we need to find the area to the left of the test statistic (z = -2.89) in the standard normal distribution.
By looking up the area in the standard normal distribution table for a z-score of -2.89, we find that the p-value is less than 0.001.
The p-value is less than 0.001.
The answer is option ⇒E
This means that the probability of observing a sample mean as extreme as 233.4 grams, assuming the population mean weight is 235 grams, is less than 0.001. Therefore, we have strong evidence to suggest that the population mean weight of bags filled by this older machine is less than 235 grams.
Your question is incomplete, but most probably the full question was:
A chip company uses machines to fill bags that are supposed to weigh 235 grams each. A quality control engineer takes the weights of 40 randomly selected bags filled by an older machine and calculates x =233.4 grams. Based on experience with machines of the same model, the company knows that σ=3.5 grams. Conduct a hypothesis test, at α=0.01, to see if there is evidence that the population mean weight of bags filled by this older machine is less than 235 grams.
-Question 4
Calculate the test statistic z, to 2 decimal places.
- Question 5
Find the p-value ...
A) 0.01
B) 0.025
C) 0.05
D) 0.1
E) 0.001