Question

In: Statistics and Probability

A random sample of 30 marathon runners demonstrated that the average age was 38 years old,...

A random sample of 30 marathon runners demonstrated that the average age was 38 years old, with s = 5 years. Find a 95% confidence interval for the average age of marathon runners.

Solutions

Expert Solution

solution

Given that,

= 38

s =5

n = 30

Degrees of freedom = df = n - 1 =30 - 1 =29

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t /2,df = t0.025,29= 2.045 ( using student t table)

Margin of error = E = t/2,df * (s /n)

=2.045 * (5 / 30) = 1.8668

The 95% confidence interval estimate of the population mean is,

- E < < + E

38 - 1.8668 < < 38+ 1.8668

36.1332 < < 39.8668

( 36.1332 , 39.8668)

orchestra answered 1 year ago
Next > < Previous

Related Solutions

The instructor claims that the average age of his students is 30 years old. To test...
The instructor claims that the average age of his students is 30 years old. To test this claim a sample of 33 students is taken. At an alpha level of .05 is there enough evidence to support this instructors claim? Sample ages: 32,28,24,18,35,41,27,28,28,31,27,25,28,31,35,40,36,32,29,28,19,21,26,24,21,19,27,26,23,27,30,20,21 Please list null and alternate hypothesis, critical value, test value, and all steps towards rejecting or accepting the null hypothesis.
World class marathon runners are known to run that distance (26.2 miles) in an average of...
World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 minutes. If we sampled a group of world class runners from a particular race, find the probability of the following: **(use 4 decimal places)** a.) The probability that one runner chosen at random finishes the race in less than 140 minutes. b.) The probability that 10 runners chosen at random have an average finish time of...
World class marathon runners are known to run that distance (26.2 miles) in an average of...
World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 15 minutes. If we sampled a group of world class runners from a particular race, find the probability of the following: **(use 4 decimal places)** a.) The probability that one runner chosen at random finishes the race in less than 140 minutes. b.) The probability that 10 runners chosen at random have an average finish time of...
World class marathon runners are known to run that distance (26.2 miles) in an average of...
World class marathon runners are known to run that distance (26.2 miles) in an average of 146 minutes with a standard deviation of 14 minutes. If we sampled a group of world class runners from a particular race, find the probability of the following: **(use 4 decimal places)** a.) The probability that one runner chosen at random finishes the race in less than 140 minutes. b.) The probability that 10 runners chosen at random have an average finish time of...
World class marathon runners are known to run that distance (26.2 miles) in an average of...
World class marathon runners are known to run that distance (26.2 miles) in an average of 143 minutes with a standard deviation of 13 minutes. If we sampled a group of world class runners from a particular race, find the probability of the following: **(use 4 decimal places)** a.) The probability that one runner chosen at random finishes the race in less than 137 minutes. b.) The probability that 10 runners chosen at random have an average finish time of...
A random sample of 20 students at a university showed an average age of 21.4 years...
A random sample of 20 students at a university showed an average age of 21.4 years and a sample standard deviation of 2.6 years. The 98% confidence interval for the true average age of all students in the university is? Enter in the upper limit of your confidence interval
A random sample of 64 students at a university showed an average age of 20 years...
A random sample of 64 students at a university showed an average age of 20 years and a sample standard deviation of 4 years. The 90% confidence interval for the true average age of all students in the university is 19.50 to 20.50 19.36 to 20.38 19.18 to 20.49 19.02 to 20.59            
The times (in seconds) for a sample of New York Marathon runners were as follows: Gender...
The times (in seconds) for a sample of New York Marathon runners were as follows: Gender Age Class Male 20-29 30-39 40+ 13615 14677 14528 18784 16090 17034 14256 14086 14935 10905 16461 14996 12077 20808 22146 Female 16401 15357 17260 14216 16771 25399 15402 15036 18647 15326 16297 15077 12047 17636 25898 Conduct a two-way analysis of variance including interactions to examine these data. Perform model criticism. What do you conclude? Note that R users do not need to...
You are 30 years old and want to retire at the age of age 65 and...
You are 30 years old and want to retire at the age of age 65 and expect to live another 25 years. On the day you retire, you want to have $900,000 in your retirement savings account. a) If you invest monthly starting one month from today and your investment earns 6.0 percent per year, How much money do you need to invest every month until you retire? b) You're retired with $900,000 and you have 25 more years. You...
A company claims its employees' mean age is 36 years old. A simple random sample of...
A company claims its employees' mean age is 36 years old. A simple random sample of 40 employees is taken, and is found to have a sample mean of 35.8 years, and sample deviation of 2.2 years. a. construct and interpret a 98% confidence interval estimate of the true population mean age. b. do you think the company's claimed mean is reasonable, based on your answer to part A? Why? c. if we assume population mean is 36, as claimed,...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT