Probability and Statistics
1. The head of the hospital maternity ward wants to estimate the average number of days a patient stays in the ward. A random sample of 100 patients showed the average stay to be 5.2 days. Using the population standard deviation of 1.9 daysfind the 90% confidence interval for the mean number of days a patient stays in the ward.
2. A random sample of 40 employee benefit packages showed that the average deductible in the employee health insurance plan was $200 with standard deviation $30. Find the 95% confidence interval for the average deductible on employee health insurance plans.
3. The data below represents the weight of a bag of salted peanuts(in ounces).
|
15.4
|
17.2
|
16.0
|
16.3
|
15.8
|
14.9
|
17.2
|
16.5
|
|
16.8
|
16.4
|
17.0
|
17.3
|
16.1
|
16.3
|
15.9
|
16.5
|
Create a 99% confidence interval for the true population mean weight of a bag of salted peanuts.
4. Carla is a realtor in a large metropolitan area. She would like to estimate the probability that a house will sell within one month of listing. From a random sample of 524 houses she found that 350 had sold within one month of listing. Create a 90% confidence interval for the proportion of houses that sell within one month of listing.
5. A survey was given to 200 high school students asking their view on the start of the school day. The results of this survey are below.
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|
Like starting before 8 a.m.
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Would like school to start after 8 a.m.
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Undecided
|
|
Number of students
|
72
|
116
|
12
|
a) Create a 99% confidence interval for the proportion of all high school students that prefer school to start after 8 a.m.
b) Create a 90% confidence interval for the proportion of all high school students that prefer school to start after 8 a.m.
c) Which interval is wider, the 90% confidence interval or the 99% confidence interval? Why do you think this is true?