Question

In: Statistics and Probability

For a school, the principal expected that a student takes 45 minutes to travel to school...

For a school, the principal expected that a student takes 45 minutes to travel to school on average. Suppose the time taken to travel to school by a student follows a normal distribution. 100 students are randomly selected from the school for interview and they took on average 44 minutes to travel to school with a standard deviation of 15 minutes. 6 of the selected students had lateness record in the last month.

  1. How large a sample is required to ensure the estimate of p is accurate within 2% with a confidence level of 97%?
  2. By using critical value approach to perform a hypothesis testing for the principal’s claim that under (10 of all students had lateness record in the last month at level of significant α = 0.01. Correct the test statistics to 2 decimal places.

Solutions

Expert Solution

The estimate of population proportion is 6/100 =0.06.

---------------------------------------------

The principal;'s claim that under 10/100 = 0.10 of all students had lateness record in the last month.

orchestra answered 2 years ago
Next > < Previous

Related Solutions

For a school, the principal expected that a student takes 45 minutes to travel to school...
For a school, the principal expected that a student takes 45 minutes to travel to school on average. Suppose the time taken to travel to school by a student follows a normal distribution. 100 students are randomly selected from the school for interview and they took on average 44 minutes to travel to school with a standard deviation of 15 minutes. 6 of the selected students had lateness record in the last month. Construct a 95% confidence interval for the...
For a travel agency clerk, it is expected to take 20 minutes to deal with a...
For a travel agency clerk, it is expected to take 20 minutes to deal with a customer. On a weekend, an average of two customers per hour arrive at the agency. Both the customer arrival times and clerk’s servicing times are modelled by an exponential distribution. a. What is the arrival rate per minute? b. What is the servicing rate per minute? c. What is the servicing rate per hour? d. What is the traffic intensity? e. What is the...
Suppose that a principal of a local high school tracks the number of minutes his students...
Suppose that a principal of a local high school tracks the number of minutes his students spend texting on a given school day. He finds that the distribution of minutes spent texting is roughly normal with a mean of 60 and a standard deviation of 20. Use this information to answer the following questions. 1. Based on the statistics, what is the probability of selecting at random a student who spends an extreme amount of time texting – either less...
Suppose that a principal of a local high school tracks the number of minutes his students...
Suppose that a principal of a local high school tracks the number of minutes his students spend texting on a given school day. He finds that the distribution of minutes spent texting is roughly normal with a mean of 60 and a standard deviation of 20. Use this information to answer the following questions. 1. Based on the statistics, find the two numbers of minutes that define the middle 95% of students in the distribution. What is the value for...
The accompanying table lists a random selection of usual travel times to​ school, in​ minutes, for...
The accompanying table lists a random selection of usual travel times to​ school, in​ minutes, for 40 secondary school students in country A. A second selection of usual travel times to​ school, in​ minutes, was randomly selected for 40 students in country B. Complete parts​ a) and​ b). Sample Country A   Sample Country B 45   29 5   10 4   9 14   30 50   5 21   8 21   7 19   15 21   10 21   36 24   16 36   10 14   24...
Assume it takes Leonardo 10 minutes to make a donut and 30 minutes to make a...
Assume it takes Leonardo 10 minutes to make a donut and 30 minutes to make a carrot cake, and it takes Emilia 12 minutes to make a donut and 24 minutes to make a carrot cake. What is the opportunity cost to Leonardo of making a donut? a. 6 carrot cakes b. 3 carrot cakes c. 1/3 of a carrot cake d. 10 carrot cakes True or False. If someone has an absolute advantage at milking goats, they will necessarily...
A manager wishes to see if the time (in minutes) it takes for their workers to...
A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will change when they are allowed to wear ear buds at work. A random sample of 25 workers' times were collected before and after. Test the claim that the time to complete the task has changed at a significance level of α=0.10. For the context of this problem, μd=μafter−μbefore where the first data set represents after and the second data...
A manager wishes to see if the time (in minutes) it takes for their workers to...
A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will decrease when they are allowed to wear ear buds at work. A random sample of 10 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed. Perform a Matched-Pairs hypothesis test for the claim that the time to complete the task has decreased at a significance level of α=0.01α=0.01. If you wish to...
A manager wishes to see if the time (in minutes) it takes for their workers to...
A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task will change when they are allowed to wear ear buds to listen to music at work. A random sample of 9 workers' times were collected before and after wearing ear buds. Assume the data is normally distributed. Perform a Matched-Pairs hypotheis T-test for the claim that the time to complete the task has changed at a significance level of α=0.01α=0.01....
A manager wishes to see if the time (in minutes) it takes for their workers to...
A manager wishes to see if the time (in minutes) it takes for their workers to complete a certain task is different if they are wearing earbuds.   A random sample of 20 workers' times were collected before and after wearing earbuds. Test the claim that the time to complete the task will be different, i.e. meaning has production differed at all, at a significance level of α = 0.01 For the context of this problem, μD = μbefore−μafter where the...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT