Question

Do low sodium hot dogs really five up to their name? A consumer watchdog organization tested 43 randomly chosen "reduced sodium" hot dogs, finding an average sodium content of 307mg with a standard deviation of 38mg. A histogram of these sodium values shows a left-skewed shape. (a) The data analyst in charge of this project is worned about the left-skeved shape. Is it valid to construct a considence interval in spite of the shewness?

Answer 1

Yes, it is valid to construct a confidence interval even if the data is left-skewed.

Step-by-step explanation:

Yes, it is valid to construct a confidence interval even if the data is left-skewed. The shape of the data distribution does not affect the validity of constructing a confidence interval. The construction of a confidence interval is based on the assumption that the sample mean follows a normal distribution due to the Central Limit Theorem, regardless of the shape of the original data distribution.

In this case, the sample mean sodium content of the hot dogs is 307mg, with a standard deviation of 38mg. To construct a confidence interval, you would use the formula:

Confidence interval = sample mean ± (critical value) × (standard deviation / √sample size)

After calculating the confidence interval, you can interpret it as a range of values within which the true population mean sodium content is likely to fall.