Question

In: Statistics and Probability

Suppose you have calculated the width of the 90% confidence interval for customer the average waiting...

Suppose you have calculated the width of the 90% confidence interval for customer the average waiting time as ± 10 minutes, based on 10 replications of your experiment. However, your boss isn’t satisfied with your choice of a 90% confidence level and wants you to run additional experiments to give him the average waiting time with a 99% confidence interval of ± 10 minutes. Approximately how many additional replications will be required? (HINT: You may assume that the sample variance doesn’t change significantly when you incorporate the data from the additional replications.)

Solutions

Expert Solution

Let X be the waiting time in minutes of any given customer.

Let s be the sample variation. The estimated value of the population variance is

The standard error of the mean for a sample of size n=10 is

The level of significance for 90% confidence interval is

The critical value of z is

which is same as

Using standard normal tables we get

The margin of error obtained for 90% confidence interval with n=10 sample is ± 10 minutes

The level of significance for 99% confidence interval is

The critical value of z is

which is same as

Using standard normal tables we get

Assuming that the sample variance remains the same, the estimate of the population standard deviation remains at

the estimate of the standard error of the mean for a sample of size n is

we want the margin of error obtained for 99% confidence interval with a sample of size n  to be  ± 10 minutes

Rounding this up, we need a sample of size n=25 to get the average waiting time with a 99% confidence interval of ± 10 minutes.

ans: We need to run 15 additional experiments to give him the average waiting time with a 99% confidence interval of ± 10 minutes.


Related Solutions

Suppose you constructed a 90% confidence interval for the true average GPA of California community college...
Suppose you constructed a 90% confidence interval for the true average GPA of California community college students. If all of the sample data were to be held constant, how would this confidence interval compare to an 80% confidence interval based on the same data? A random sample of 100 students was taken to determine interest in switching to a quarter system instead of semesters. Out of the 100 students, 73 stated that they were interested in switching to a quarter...
If you wanted to calculate a 90% confidence interval for the difference in average number of...
If you wanted to calculate a 90% confidence interval for the difference in average number of friendship contacts between primary aged boys and girls and we are pretending that df=12, what t scores would you use? (assuming equal variances again) A. ☐+/- 1.356 B. ☐+/- 2.681 C. ☐+/- 1.782 D. ☐+/- 2.179 E. ☐+/- 3.055 9. Suppose you calculated your 90% interval as described above and your lower confidence limit was –2.75 and your upper confidence limit was 3.20. What...
You are interested in finding a 90% confidence interval for the average number of days of...
You are interested in finding a 90% confidence interval for the average number of days of class that college students miss each year. The data below show the number of missed days for 14 randomly selected college students. Round answers to 3 decimal places where possible. 1 8 10 9 1 3 1 8 1 0 2 1 5 8 a. To compute the confidence interval use a distribution. b. With 90% confidence the population mean number of days of...
A student was asked to find a 90% confidence interval for widget width using data from...
A student was asked to find a 90% confidence interval for widget width using data from a random sample of size n = 20. Which of the following is a correct interpretation of the interval 11.8 < μ < 21.7? Check all that are correct. The mean width of all widgets is between 11.8 and 21.7, 90% of the time. We know this is true because the mean of our sample is between 11.8 and 21.7. With 90% confidence, the...
As the sample size INCREASES for computing a confidence interval, the width of the confidence interval...
As the sample size INCREASES for computing a confidence interval, the width of the confidence interval DECREASES. 12 When the population standard deviation sigma is assumed known, a confidence interval can assume NORMALITY of the SAMPLE MEAN if the sample size is greater than 30. 12 A SYMMETRIC histogram implies the plotted variable is NORMALLY distributed. 12 The goal when using confidence intervals is to have WIDE INTERVALS to be assured that the interval contains the population parameter. 12 A...
You are interested in finding a 90% confidence interval for the average commute that non-residential students...
You are interested in finding a 90% confidence interval for the average commute that non-residential students have to their college. The data below show the number of commute miles for 11 randomly selected non-residential college students. Round answers to 3 decimal places where possible. 25 21 26 6 25 14 26 24 7 10 14 a. To compute the confidence interval use a distribution. b. With 90% confidence the population mean commute for non-residential college students is between and miles....
Part 1. Suppose you are told that a 95% confidence interval for the average price of...
Part 1. Suppose you are told that a 95% confidence interval for the average price of a gallon of regular gasoline in your state is from $2.99 to $3.99. Use the fact that the confidence interval for the mean is in the form x − E to x + E to compute the sample mean and the maximal margin of error E. (Round your answers to two decimal places.) x = $ E = $ Part 2. Anystate Auto Insurance...
A sample is selected to find a 90% confidence interval for the average starting salary. Here...
A sample is selected to find a 90% confidence interval for the average starting salary. Here are the sample statistics: n = 31, x ̄ = $43, 780, s = $1, 600. a). Find the t− score used in the calculation of the confidence interval. b). Build a 90% confidence interval for the mean starting salary. c). Based on the result of part b), could we make a conclusion that the mean staring salary is below $45, 000? Explain your...
If you had found a 90% confidence interval for µ, how would it have differed from...
If you had found a 90% confidence interval for µ, how would it have differed from the 95% confidence interval?
Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that...
Please calculate the 90% Confidence Interval for the population slope in the following scenario. Suppose that you collected data to determine the relationship between the amount of time a person spends online as an independent variable and the amount of money a person spends online as the dependent variable. Use the following data for questions 6, 7, 8, 9, & 10. The regression equation is = 24 + 10.1x, where x represents the number of hours a person spends online...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT