Test of Single Mean of Large Sample Test - Problem 3 - Sampling Theory - Engineering Mathematics 4

TL;DR

The average lifespan of an Indian is concluded to be more than 70 years based on a random sample of 100 Indians with an average lifespan of 71.8 years and a standard deviation of 7.8 years.

Transcript

hello friends in this video we'll be discussing the third problem on type one of large sample test that is test for single mean let us read the problem first can it be concluded that the average life span of an Indian is more than 70 years if a random sample of 100 Indians has an average lifespan of 70 one point eight years with standard deviation ... Read More

Key Insights

• 🌥️ The problem requires a large sample test to determine the average lifespan of Indians.
• ❓ The provided sample data suggests that the average lifespan is more than 70 years.
• 😫 The analysis involves setting null and alternate hypotheses, determining the level of significance, calculating the test statistic, and making a conclusion based on the critical value.

Questions & Answers

Q: What is the purpose of the large sample test for a single mean?

The purpose is to determine whether the average of a population is significantly different from a given value, using a random sample with a sample mean and standard deviation.

Q: Why is it necessary to set null and alternate hypotheses?

The null hypothesis states that the population mean is equal to the given value, and the alternate hypothesis asserts that the population mean is not equal to the given value. These hypotheses guide the statistical analysis and help in making a conclusion.

Q: How is the level of significance determined in the analysis?

The level of significance, also known as alpha (α), is chosen based on the desired confidence level. In this case, a 5% level of significance is used, corresponding to a significance level of 0.05.

Q: How is the test statistic calculated in the large sample test?

The test statistic (Z) is calculated using the formula Z = (X bar - mu) / (Sigma / sqrt(n)), where X bar is the sample mean, mu is the population mean, Sigma is the population standard deviation, and n is the sample size.

Summary & Key Takeaways

• The problem discusses the question of whether the average life span of an Indian is more than 70 years, based on a random sample of 100 Indians.

• The sample data suggests that the average life span is indeed more than 70 years, but further analysis is required to draw a conclusion for the entire population.

• The analysis involves setting null and alternate hypotheses, determining the level of significance, calculating the test statistic, and making a conclusion based on the critical value.