Always remember to interpret your solutions.
The manager of a large factory wants to know the average hourly wage of its employees. From a sample of 200 employees the sample mean wage was $9.97 per hour with a standard deviation of $1.42.Calculate a 90% confidence interval for the mean.
We are 90% confident the average hourly wage for all factory employees is between $9.81 and $10.14.
If one wanted an interval that contains at least 90% of the hourly wages for the company how would the calculations be different?This range must contain 90% employees" hourly wages, rather than the mean hourly wage. This can be answered by using the empirical rule, if the wages are normally distributed, or Chebyshev's rule, if they are not. Both rules find a range of values by adding and subtracting a number of standard deviations to and from the mean rather than a number of standard errors.The president of a company, who owns and operates movie theatres in Wyoming, is concerned about his business. Due to the simplicity of going out and renting a movie to watch at home, the number of people going to see movies in the theatre is steadily declining. He directs his staff to conduct a study in order to estimate the mean number of movies people in Wyoming rented during December. After conducting a phone survey, the staff found that the mean number for 300 randomly selected people was 2.4 with a standard deviation of 1.6. What is the true mean with 95% confidence? .
We are 95% confident the mean number of movies rented by people in Wyoming during the month of December is between 2.22 and 2.58.The president then wants to know the proportion of people who rent at least 2.5 movies per month. Assume that the distribution of the number of movies rented is normal with a mean and standard deviation approximately the same as what was obtained in the sample.
Approximately 47.61% of people in Wyoming rent more than 2.5 movies per month.