Question

Construct a 95% confidence interval estimate for the population mean amount spent for lunch ($) at a fast-food restaurant. Round to two decimal places as needed.

Answer 1

The 95% confidence interval estimate for the population mean amount spent for lunch ($) at a fast-food restaurant is approximately between $X and $Y.

Step-by-step explanation:

To construct a 95% confidence interval for the population mean amount spent for lunch at a fast-food restaurant, statistical methods are employed. The interval is calculated based on a sample mean and the standard error of the mean. The formula for the confidence interval is:

`\[ \text{Confidence Interval} = \text{Sample Mean} \pm \left( \text{Critical Value} * \text{Standard Error} \right) \]`

The critical value is determined by the desired confidence level and the degrees of freedom. For a 95% confidence interval with a normal distribution, the critical value is approximately 1.96. The standard error is a measure of the variability of the sample mean and is calculated using the sample standard deviation and the square root of the sample size.

The resulting interval provides a range of values within which we can be 95% confident that the true population mean amount spent for lunch lies. This means that if we were to take many random samples and construct confidence intervals for each, about 95% of these intervals would contain the true population mean.

The precision of the interval is influenced by the sample size; larger samples tend to result in narrower intervals. Therefore, the 95% confidence interval gives a sense of the likely range for the average amount spent for lunch at a fast-food restaurant based on the sample data.Answer: