Question

In: Statistics and Probability

In a study of the length of time it takes to earn an associate’s degree, a...

In a study of the length of time it takes to earn an associate’s degree, a random sample of 41 students had a mean of 2.8 years. Assume that the population standard deviation is 0.9 years. You wish to construct a 99% confidence interval for the mean time it takes to earn an associate's degree. Use this information to answer the next 5 questions. (Be sure to use the correct distribution.)

What is the confidence interval? Round to 2 decimal places.

If applicable, what are the degrees of freedom? (Type NA if not applicable.)

What is the critical value?

What is the point estimate?

What is the margin of error? Round to 2 decimal places.

Solutions

Expert Solution

Solution :

Given that,

1) Point estimate = sample mean = = 2.8 years

Population standard deviation =    = 0.9 years

Sample size = n = 41

2) degrees of freedom = NA

3) At 99% confidence level

= 1 - 99%  

= 1 - 0.99 =0.01

/2 = 0.005

Z/2 = Z0.005 = 2.576


4) Margin of error = E = Z/2 * ( /n)

E = 2.576 * ( 0.9 /  41 )

E = 0.36

5) At 99% confidence interval estimate of the population mean is,

  ± E

2.8 ± 0.36

( 2.44, 3.16 )  

orchestra answered 1 year ago
Next > < Previous

Related Solutions

*Generation time can best be defined as a. the length of time it takes for lag...
*Generation time can best be defined as a. the length of time it takes for lag phase b. the duration of log phase c. the time it takes for a cell to divide d. how many generations a cell can divide *Bacterial growth is usually graphed using ________. a. an arithmetic plot. b. a hyperbolic plot. c. a semi-logarithmic plot. d. an inverse plot. *Most bacteria reproduce by a. aerial hyphae. b. fragmentation. c. mitosis. d. binary fission. e. budding....
The length of time it takes a baseball player to swing a bat (in seconds) is...
The length of time it takes a baseball player to swing a bat (in seconds) is a continuous random variable X with probability density function (p.d.f.) f(x) = ( ax + 8/9 for 0 ≤ x ≤ b (c) Calculate (to 3 decimal places of accuracy) the median of X. (d) What is the probability that the baseball player takes between 5 and 10 swings (inclusive) before a swing whose length is greater than the median in part (c) occurs...
The length of time, in hours, it takes an "over 40" group of people to play...
The length of time, in hours, it takes an "over 40" group of people to play one soccer match is normally distributed with a mean of 2.2 hours and a standard deviation of 0.55 hours. A sample of size n = 80 is drawn randomly from the population. Find the probability that the sample mean is between 2.1 hours and 2.4 hours.
Let 'x' be a random variable that represents the length of time it takes a student...
Let 'x' be a random variable that represents the length of time it takes a student to write a term paper for Dr. Adam's Sociology class. After interviewing many students, it was found that 'x' has an approximately normal distribution with a mean of µ = 7.3 hours and standard deviation of ơ = 0.8 hours. For parts a, b, c, Convert each of the following x intervals to standardized z intervals. a.) x < 8.1   z < b.) x...
1. (15pts) The length of time it takes to get through the security checks at a...
1. (15pts) The length of time it takes to get through the security checks at a very large urban airport is a random variable with mean μ = 20.6 minutes and standard deviation σ = 8.4 minutes. A simple random sample of 36 airline passengers is to be observed going through security. ̄ a) What is the sampling distribution of the sample mean X? (Specify the distribution,mean μX ̄ and standard deviation σX ̄ of the sampling distribution of X)...
The length of time it takes to find a parking space at 9 a.m. follows a...
The length of time it takes to find a parking space at 9 a.m. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. a) Based upon the empirical rule, which is the probability that it takes less than one minute to find a parking space? b) Based upon the empirical rule, which is the probability that it takes more than 7 minutes to find a parking space? c) Find the probability that...
The length of time it takes to find a parking space at 8am follows a normal...
The length of time it takes to find a parking space at 8am follows a normal distribution with a mean of 10 minutes and a standard deviation of 3 minutes. 1.Find the probability that it takes at most five minutes to find a parking space. 2.Find the probability that it takes at least 13 minutes to find a parking space. 3.Find the probability that it takes between 9 minutes to 11 minutes find a parking space. 4.25% of the time,...
The length of time, in hours, it takes an "over 40" group of people to play...
The length of time, in hours, it takes an "over 40" group of people to play one soccer match is normally distributed with a mean of 4 hours and a standard deviation of 0.5 hours. A sample of size n = 50 is drawn randomly from the population. Find the probability that the sample mean is between 3.5 hours and 4.1 hours.
A study of the amount of time it takes a mechanic to rebuild the transmission for...
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2010 Chevrolet Colorado shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly​ selected, find the probability that their mean rebuild time is less than 8.9 hours. Round to four decimal places. A.0.9756 B.0.9605 C.0.4276 D.0.9589
A study of the amount of time it takes a mechanic to rebuild the transmission for...
A study of the amount of time it takes a mechanic to rebuild the transmission for a 2005 Chevrolet Cavalier shows that the mean is 8.4 hours and the standard deviation is 1.8 hours. If 40 mechanics are randomly selected, find the probability that their mean rebuild time exceeds 8.7 hours. Group of answer choices
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT