Final answer:
- a. The critical value, tal 2, is 2.73.
- b. The margin of error is approximately 1890 g.
- c. The confidence interval estimate of u is approximately 2882.8 g to 5087.2 g.
Step-by-step explanation:
To find the margin of error, we need to multiply the critical value by the standard deviation of the sample. In this case, the critical value is given as 2.73 and the standard deviation (s) is 692.6 g.
(a) The critical value is specific to the chosen confidence level and the degrees of freedom in the problem. In this case, the value 2.73 is provided as the critical value.
Based on the given information, the critical value tal 2 is 2.73.
(b) The margin of error, E, can be calculated by multiplying the critical value by the standard deviation:
E = tal 2 * s
E = 2.73 * 692.6 g
E ≈ 1889.9 g
E ≈ 1890 g (rounded to one decimal place)
Therefore, the margin of error is approximately 1890 g.
(c) The confidence interval estimate of u (the population mean) can be found by subtracting and adding the margin of error from the sample mean (x).
- Confidence interval = x ± E
- Confidence interval = 3197.2 g ± 1890 g
- Lower bound = x - E
- Lower bound = 3197.2 g - 1890 g
- Lower bound ≈ 1307.2 g
- Upper bound = x + E
- Upper bound = 3197.2 g + 1890 g
- Upper bound ≈ 5087.2 g
Therefore, the confidence interval estimate of u is approximately 2882.8 g to 5087.2 g.
Your question is incomplete, but most probably the full question was:
Here are summary statistics for randomly selected weights of newborn girls: n= 36, x = 3197.2 g, s = 692.6 g.
Use a confidence level of 99% to complete parts (a) through (c) below.
- a. Identify the critical value tal 2 used for finding the margin of error. tal2 = 2.73 (Round to two decimal places as needed.)
- b. Find the margin of error. E= 314.4 g (Round to one decimal place as needed.)
- c. Find the confidence interval estimate of u. 2882.8 g<u< 3511.69 g (Round to one decimal place as needed.)