Final Answer:
The 95% confidence interval estimate for the average length across shells of all giant clams is approximately between 43.36 inches and 46.64 inches.
Step-by-step explanation:
The 95% confidence interval is a statistical range that provides an estimate of where the true population parameter is likely to be. In this case, we are estimating the average length across shells of all giant clams based on a sample of 10 clams. The average length of the sample is 45 inches, and the standard deviation is 4 inches.
To construct the confidence interval, we use the formula:
\[ \text{Confidence Interval} = \text{Sample Mean} \pm (\text{Critical Value} \times \text{Standard Error}) \]
The critical value is determined based on the desired confidence level and the degrees of freedom, which is n-1 for a sample of size n. In this case, with a 95% confidence level and 9 degrees of freedom, the critical value is obtained from a t-distribution.
The standard error is calculated as the standard deviation divided by the square root of the sample size. Plugging in the values, we get a confidence interval of approximately 43.36 to 46.64 inches. This means that we can be 95% confident that the true average length across shells of all giant clams falls within this range based on the given sample.