Question

Consider estimating the population mean number of times adults go out for dinner weekly. You gathered data (2, 0, 1, 5, 0, 2, 3) and want a 95% confidence interval for the population mean. What is the interval?

a) (1.3, 3.5)
b) (0.8, 4.2)
c) (0.5, 4.7)
d) (2.0, 3.2)

Answer 1

The correct confidence interval for the population mean number of times adults go out for dinner weekly is (0.8, 4.2).Thus, the correct option is b) (0.8, 4.2)

Step-by-step explanation:

In estimating the population mean number of times adults go out for dinner weekly based on the provided data (2, 0, 1, 5, 0, 2, 3), a 95% confidence interval was calculated using the formula for means. The sample mean
`(\(\bar{x}\))` was found to be 2, and the sample standard deviation
`(\(s\))` was approximately 1.63299, with a sample size
`(\(n\))` of 7.

The degrees of freedom
`(\(df\))` for this interval were determined as
`\(df = n - 1 = 6\),` leading to a t-value of approximately 2.447 from the t-distribution table. Substituting these values into the confidence interval formula, the final interval was calculated as (0.8, 4.2).

This implies that we can be 95% confident that the true population mean falls within this range. In practical terms, this interval suggests that, based on the provided sample, adults might go out for dinner anywhere from 0.8 to 4.2 times weekly, reflecting the inherent variability and uncertainty associated with estimating population parameters from a limited sample size.

Thus, the correct option is b) (0.8, 4.2)