"In Problems 23 through 26, indicate whether a confidence interval for a proportion or mean should be constructed to estimate the value of the variable of interest. Justify your response.
Does chewing your food for a longer period of time reduce one’s caloric intake of food at dinner? A researcher requires a sample of 75 healthy males to chew their food twice as long as they normally do. The researcher then records the calorie consumption at dinner."

Verified step by step guidance

1. Step 1: Identify the type of variable being measured. In this problem, the researcher records the calorie consumption at dinner, which is a numerical value representing the amount of calories consumed.
2. Step 2: Determine whether the variable is quantitative or categorical. Since calorie consumption is a numerical measurement, it is a quantitative variable.
3. Step 3: Decide whether to construct a confidence interval for a mean or a proportion. Confidence intervals for means are used when estimating the average value of a quantitative variable, while confidence intervals for proportions are used when estimating the proportion of a population with a certain characteristic (categorical variable).
4. Step 4: Since the variable of interest (calorie consumption) is quantitative, the appropriate confidence interval to construct is for the mean calorie consumption of the population of healthy males chewing their food longer.
5. Step 5: Justify the choice by stating that the goal is to estimate the average calorie intake, which is a mean, not a proportion, so a confidence interval for the mean should be constructed.

Key Concepts

Confidence Interval

A confidence interval estimates a population parameter (mean or proportion) by providing a range of plausible values based on sample data. It reflects the uncertainty inherent in sampling and is typically expressed with a confidence level, such as 95%, indicating the probability that the interval contains the true parameter.

Mean vs. Proportion

A mean is the average value of a quantitative variable, while a proportion represents the fraction of observations with a specific categorical outcome. Determining whether to construct a confidence interval for a mean or proportion depends on whether the variable of interest is numerical (e.g., calories consumed) or categorical (e.g., yes/no responses).

Sampling and Data Type Identification

Understanding the type of data collected from the sample is crucial for selecting the correct statistical method. In this case, calorie consumption is a continuous numerical variable, so the sample of 75 males provides data suitable for estimating the mean calorie intake, not a proportion.