In an experiment to assess the strength of the hunger drive...

In an experiment to assess the strength of the hunger drive in rats, 30 previously trained animals were deprived of food for 24 hours. At the end of the 24 -hour period, each animal was put into a cage where food was dispensed if the animal pressed a lever. The length of time the animal continued pressing the bar (although receiving no food) was recorded for each animal. If the data yielded a sample mean of 19.3 minutes with a standard deviation of 5.2 minutes, estimate the true mean time and calculate the margin of error.

Key Concepts

Student's t-Distribution

When the population standard deviation is unknown and the sample size is relatively small, the Student's t-distribution is used instead of the normal distribution to determine critical values for constructing confidence intervals. The t-distribution accounts for additional uncertainty and converges to the normal distribution as the sample size increases.

Confidence Interval

A confidence interval provides a range of values that is believed, with a certain degree of confidence (e.g., 95%), to contain the true population parameter. It combines the point estimate and the margin of error to express the uncertainty inherent in using sample data to estimate population parameters.

Margin of Error

The margin of error represents the range within which the true population parameter is expected to lie with a given level of confidence. It is derived by multiplying a critical value (from a probability distribution) by the standard error. This concept is fundamental in constructing confidence intervals.

Standard Deviation and Standard Error

Standard deviation measures the spread or dispersion of the data points in the sample, indicating how much the individual observations vary from the sample mean. The standard error, often calculated by dividing the standard deviation by the square root of the sample size, quantifies the variability of the sample mean if the sampling were repeated multiple times.

Population Parameter Estimation

This concept involves estimating an unknown characteristic (such as the true mean) of the entire population based on information obtained from a sample. In inferential statistics, we use sample data to make inferences about a population parameter, acknowledging that the sample is only a subset of the total population.

Sample Mean

The sample mean is the arithmetic average of the observed values in the sample and serves as a point estimate for the unknown population mean. It is calculated by summing all the sample observations and dividing by the number of observations.

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