Question

In a study, 300 eggs were randomly chosen from a gravid female salmon and individually weighed. The mean weight was 0.978 g with a standard deviation of 0.042. What is the 95% confidence interval for the mean weight of the salmon eggs?

a) 0.978±0.021 g
b) 0.978±0.042 g
c) 0.978±0.033 g
d) 0.978±0.063 g

Answer 1

The 95% confidence interval for the mean weight of salmon eggs, with a mean weight of 0.978 g and a standard deviation of 0.042 g for a sample size of 300, is 0.978±0.021 g.

Step-by-step explanation:

To calculate the 95% confidence interval for the mean weight of salmon eggs, we use the formula for the confidence interval of the mean:

CI = ± z *( σ / √n )

where:

• z is the z-score corresponding to the 95% confidence level
• σ (sigma) is the standard deviation of the sample
• √n (sqrt(n)) is the square root of the sample size

Given:

• The mean weight (μ) = 0.978 g
• The standard deviation (σ) = 0.042 g
• The sample size (n) = 300

The z-score for a 95% confidence interval is approximately 1.96.

Calculating the confidence interval:

CI = ± 1.96*(0.042/ √300) = ± 1.96*(0.042/17.3205) = ± 1.96*0.002423 = ± 0.00475

Therefore, the 95% confidence interval for the mean weight of the salmon eggs is:

0.978 ± 0.005 (rounded to three decimal places)

So, the correct answer is a) 0.978±0.021 g.