The lifetime of a particular component is normally distributed with a mean of 1,000 hours anda standard deviation of 100 hours. Make the following calculations:
a.) If a random sample of 9 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050?
b.) If a random sample of 25 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050?
c.) If a random sample of 100 components are taken from the population, what is the probability that the sample mean will lie between 950 and 1050?
a). Of 900 customers surveyed, 414 said they were very enthusiastic about a new home decor scheme. Construct a 99 percent confidence interval estimate of the population proportion.
Interpret your answer.
b.) A sample of 49 vehicles are taken, measuring the speed of the vehicle at a specific point.The sample mean was 55, and the standard deviation fo the sample was 10. What is the 90 percent confidence interval estimate of the mean speed of vehicles at this point?
c.) The attendance at the Nashville minor league baseball game last night was 400. A random sample of 50 of those in attendance revealed that the mean number of soft drinks consumed was 3.24, with a standard deviation of 0.50. Develop a 95 percent confidence interval estimate of the mean. Interpret your answer.
d.) A sample survey of the 256 largest companies in the U.S. found that 23 percent had told their employees how the economic downturn in early 2001 would affect the organization. Can you form a 99 percent confidence interval estimate of the proportion of all firms in the U.S. that informs their employees of the effects of recession?
a.) To help your restaurant marketing campaign target the right age levels, you want to find out if there is a statistically signicant difference between the mean age of your customers and the age of the general population in your town: 43.1 years. A random sample of 50 of your customers shows a mean of 33.6 years and a standard deviation of 16.2 years. Test at a .05 level of significance.
b.) Part of the assembly line will need adjusting if the consistency of the injected plastic becomes either viscous or not viscous enough as compared with a value (56.00) your engineers consider optimal. You will decide to adjust only if you are convinced that the system is not in control; that is, there is a real need for adjustment. The average viscosity for 13 recent measurements was 51.22 with a standard deviation of 3.18. Test at = .01.
c.) Your Detroit division produced 135 defective parts out of the total production of 983 last week. The Kansas City division produced 104 defectives out of 1,085 produced in the same time period. Is the dierence in defective rates between the two divisions statistically significant? Test at a .05 level.