The mean age at which men in the United States marry for the...

Name: Problem 35, Chapter 8: Basic Statistics for Business and Economics
Uploaded: 2022-03-26T15:00:18-08:00
Duration: 2 min 37 s
Channel: Sheryl Ezze
Description: The mean age at which men in the United States marry for the first time is 24.8 years. The shape and the standard deviation of the population are both unknown. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.1 years? Assume that the standard deviation of the sample is 2.5 years.

The mean age at which men in the United States marry for the first time is 24.8 years. The shape and the standard deviation of the population are both unknown. For a random sample of 60 men, what is the likelihood that the age at which they were married for the first time is less than 25.1 years? Assume that the standard deviation of the sample is 2.5 years.

Key Concepts

Central Limit Theorem

This theorem states that the distribution of the sample mean tends to be normal (or nearly normal) when the sample size is sufficiently large, regardless of the shape of the population distribution. It allows us to use normal approximation techniques in probability calculations for sample means, even when the underlying population distribution is unknown.

Sampling Distribution of the Mean

This concept refers to the probability distribution of the sample mean, computed from all possible samples of a fixed size drawn from a population. Its mean is the same as the population mean, and its variability is measured by the standard error. Understanding the sampling distribution is crucial for making inferences about the population.

Standard Error

The standard error quantifies the variability of the sample mean by dividing the sample standard deviation by the square root of the sample size. It reflects how accurately the sample mean approximates the true population mean and is essential in determining the probability of observing a sample mean within a certain range.

t-distribution

When the population standard deviation is unknown and the sample size is not extremely large, the t-distribution is used instead of the normal distribution to account for additional uncertainty from estimating the standard deviation. This distribution is similar to the normal distribution but has heavier tails, which means it provides wider confidence intervals and more conservative probability estimates.

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