You observe a sample of five numbers between 0 and 10. Their median is 5 and their mean is 5. What is the maximum and minimum possible variance of the numbers? (No formal calculation or proof is expected. Please explain your reasoning in one to two sentences and report the 5 numbers that give you the lowest variance and the 5 numbers that give you the highest variance.)

What is the best point estimate for the population's variance if the sample variance is 41?

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 205 Fundash runners and 300 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 205 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.3 minutes. The 300 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.1 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, ,, of Fundash is not equal to the mean completion time, μ₂, of Coolsprint? Perform a two-tailed test.…

Problem: The number of misdirected luggage cases reported for 5 consecutive weeks at the domestic airport were:   4, 5, 7, 8, 61. Compute the Mean, Median, Range, Interquartile Range, Variance and Standard deviation.

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 250 Fundash runners and 285 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 250 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.7 minutes. The 285 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.6 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, u, of Fundash is not equal to the mean completion time, µa, of Coolsprint? Perform a two-tailed test.…

A bank has a Head Office in Delhi and a branch at Mumbai. There are long customer queues at one office, while customer queues are short at the other office. The Operations Manager of the bank wonders if the customers at one branch are more variable than the number of customers at another branch. A research study of customers is carried out by him. The variance of Delhi Head Office customers is 31 and that for Mumbai branch is 20. The sample size for Delhi Head Office is 11 and that for Mumbai branch is 21. Use a 5 % level of significance to test the difference in variance for both the branches.

A sample of n = 10 has s = 3. What are the correct values for S.S. and s2? SS=44;sampleS.D.=3 SS = 81; sample variance = 9 SS = 30; sample variance = 4 SS=27;sampleS.D.=2

I am having trouble with this one, please help. Thank you

Describe a study in which you can use both nonparametric and parametric statistics. A researcher has participants expecting to receive either painful or mild electrical shocks during a study wait in a quarter-full waiting room with other participants. He then measures whether they choose to sit next to other participants or if they sit far away on their own. What is the best test to run for this study and why?

An adventure company runs two obstacle courses, Fundash and Coolsprint. The designer of the courses suspects that the mean completion time of Fundash is not equal to the mean completion time of Coolsprint. To test this, she selects 240 Fundash runners and 200 Coolsprint runners. (Consider these as random samples of the Fundash and Coolspring runners.) The 240 Fundash runners complete the course with a mean time of 76.7 minutes and a standard deviation of 5.2 minutes. The 200 Coolsprint runners complete the course with a mean time of 77.5 minutes and a standard deviation of 5.4 minutes. Assume that the population standard deviations of the completion times can be estimated to be the sample standard deviations, since the samples that are used to compute them are quite large. At the 0.05 level of significance, is there enough evidence to support the claim that the mean completion time, μ1 , of Fundash is not equal to the mean completion time, μ2 , of Coolsprint?…