Homework SourseI already have the answers written in just checking if corre
(I already have the answers written in just checking if correct before I submit it)
Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 40 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.1171 seconds. The standard deviation of the search times for the sample was calculated as 0.0162 seconds. The population standard deviation of search times is unknown.
a)Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation (?) is unknown:
b)Calculate the upper and lower bounds of the 95% confidence interval for the mean search time for the Gurgle search engine. You may find this Student\'s t distribution table useful. Give your answers in seconds to 4 decimal places.
Upper bound = 0.2223 seconds
Lower bound = 0.1119 seconds
| Approximate the population standard deviation (?) with the sample standard deviation (s) | |
| Replace the sample size (n) with n-1 | |
| Decrease the confidence level to compensate for the increased margin of error | |
| Approximate the standard normal distribution with the Student\'s t distribution |
Solution
(I already have the answers written in just checking if correct before I submit it)
Internet company Gurgle is carrying out testing on the efficiency of its search engine. A sample of 40 searches have been carried out and the time taken to display the results has been recorded for each search. The mean search time for the sample was calculated as 0.1171 seconds. The standard deviation of the search times for the sample was calculated as 0.0162 seconds. The population standard deviation of search times is unknown.
a)Select all the techniques that are commonly used to construct a confidence interval for the mean when the population standard deviation (?) is unknown:
Approximate the population standard deviation (?) with the sample standard deviation (s)
Replace the sample size (n) with n-1
Decrease the confidence level to compensate for the increased margin of error
Approximate the standard normal distribution with the Student\'s t distribution
b)Calculate the upper and lower bounds of the 95% confidence interval for the mean search time for the Gurgle search engine. You may find this Student\'s t distribution table useful. Give your answers in seconds to 4 decimal places.
Upper bound = 0.1223 seconds
Lower bound = 0.1119 seconds
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
0.0162
Sample Mean
0.1171
Sample Size
40
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
0.002561445
Degrees of Freedom
39
t Value
2.0227
Interval Half Width
0.0052
Confidence Interval
Interval Lower Limit
0.1119
Interval Upper Limit
0.1223
| Approximate the population standard deviation (?) with the sample standard deviation (s) | |
| Replace the sample size (n) with n-1 | |
| Decrease the confidence level to compensate for the increased margin of error | |
| Approximate the standard normal distribution with the Student\'s t distribution |
