Sample Mean Hypothesis Testing

Imagine that you have a portfolio of stocks. You want to compare the performance of your stocks to the market as a whole. You learn that the population mean,μ, of stock returns is 7%, and that the population standard deviation, σ, is 2%.

1. Imagine that you have a portfolio of 10 stocks, that have a sample mean of 14%. Construct a 90% confidence interval.
   What is the probability that the sample mean is equal to the population mean?
2. Imagine that you have a portfolio of 10 stocks, that have a sample mean of 2% returns. Construct a 95% confidence interval.
3. What is the probability that the sample mean is equal to the population mean?
4. Imagine that you have a portfolio of 10 stocks, that have a sample mean of 8%, what is the probability that the sample mean is equal to the population mean?

Sample Proportion Hypothesis Testing

Individuals are often classified as being morbidly obese if they are 100 pounds overweight. Imagine that the population proportion of morbidly obese individuals in the country as a whole is 2%.

1. How large does n need to be to use the standard normal distribution?
2. You obtain information on 500 individuals from a town and calculate the sample proportion to be 4%.
3. Calculate a 90% confidence interval for sample proportion?
4. Does the confidence interval include the population proportion?
5. What is the probability that the sample proportion is equal to the population proportion?