Question
In: Statistics and Probability
A college admissions director wishes to estimate the mean age of all students currently enrolled. In...
A college admissions director wishes to estimate the mean age of all students currently enrolled. In a random sample of 81 students, the mean age is found to be 20.51 years. From past studies, the standard deviation of the population is known to be 2 years, and the population is normally distributed. Construct a 99% confidence interval of the population mean age. (Round off final answers to two decimal places, if appropriate. Do not round off numbers taken directly from tables).
Solutions
Expert Solution
Solution :
Given that,
sample size = n = 81
Degrees of freedom = df = n - 1 = 81 - 1 = 80
t
/2,df = 2.639
Margin of error = E = t/2,df
* (s /
= 2.639 * (2 /
Margin of error = E = 0.59
The 99% confidence interval estimate of the population mean is,
- E < 
<
+ E
20.51 - 0.59 <
< 20.51 + 0.59
19.92 <
< 21.10
A 99% confidence interval of the population mean: (19.92 , 21.10)
orchestra answered 2 years agoRelated Solutions
A college admissions director wishes to estimate the mean age of all students currently enrolled. In...
A college admissions director wishes to estimate the mean age of
all students currently enrolled. In a random sample of 19 students,
the mean age is found to be 22.4 years. From past studies, the ages
of enrolled students are normally distributed with a standard
deviation of 9.5 years. Construct a 90% confidence interval for the
mean age of all students currently enrolled.
1. What is the critical value?
2. What is the standard deviation of the sample mean?
3....
A college admissions director wishes to estimate the mean age of all students currently enrolled. In...
A college admissions director wishes to estimate the mean age
of all students currently enrolled. In a random sample of 19
students, the mean age is found to be 22.4 years. From past
studies, the ages of enrolled students are normally distributed
with a standard deviation of 9.5 years. Construct a 90% confidence
interval for the mean age of all students currently enrolled.
1. what is the critical value ?
2. the margin of error?
A college admissions director wishes to estimate the mean age of all students currently enrolled. In...
A college admissions director wishes to estimate the mean age of
all students currently enrolled. In a random sample of 22 students,
the mean age is found to be 21.4 years. From past studies, the ages
of enrolled students are normally distributed with a standard
deviation of 10.2 years. Construct a 90% confidence interval for
the mean age of all students currently enrolled.
b. The standard deviation of the sample mean:
An admissions director wants to estimate the mean age of all students enrolled at a college....
An admissions director wants to estimate the mean age of all
students enrolled at a college. The estimate must be within 1 years
of the population mean. Assume the population of ages is normally
distributed and the population standard deviation is 9.5 years.
Determine the minimum sample size required to construct a 80%
confidence interval for the population mean age. Determine the
minimum sample size required to construct a 95% confidence interval
for the population mean age. Which level of...
The admission office wants to estimate the mean age of all students enrolled at ZU. The...
The admission office wants to estimate the mean age of all
students enrolled at ZU. The estimate must be within half year of
the population mean. Assume the population of ages is normally
distributed. Also assume that the population standard
deviation is 1.4 years.
1- Determine the minimum sample size required to construct a 90%
confidence interval for the population mean ?....
2-Repeat part (a) using a 99% confidence interval ? .....
3-Which level of confidence requires a larger sample
size?...
A college admissions officer for the school’s online undergraduate program wants to estimate the mean age...
A college admissions officer for the school’s online
undergraduate program wants to estimate the mean age of its
graduating students. The administrator took a random sample of 40
from which the mean was 24 years and the standard deviation was 1.7
years.
If the mean age of online undergraduate students was 23 years of
age, what is the probability that the sample of 40 would have
produced a mean age of 24 or higher? Be sure to set up the...
The director of admissions of a small college selected 120 students at random from the new...
The director of admissions of a small college selected 120
students at random from the new freshman class in a study to
determine whether a student's grade point average (gpa) at the end
of freshman year can be predicted from the ACT test score.
(a) Read in the dataset (it is in the le named ACT.txt ).
(b) Obtain the least-squares estimates of intercept and slope,
and state the estimated regression function.
(c) Plot the data and the estimated regression...
The director of admissions of a small college selected 120 students at random from the new...
The director of admissions of a small college selected 120
students at random from the new freshman class in a study to
determine whether a student’s grade point average (GPA) at the end
of the freshman year (y) can be predicted from the ACT test score
(x1).
GPA ACT ITS RP
3.897 21 122 99
3.885 14 132 71
3.778 28 119 95
2.540 22 99 75
3.028 21 131 46
3.865 31 139 77
2.962 32 113 85...
The president of a University wishes to find the average age of students presently enrolled. From...
The president of a University wishes to find the average age of
students presently enrolled. From past studies, the standard
deviation is known to be 2 years. A random sample of 50 students is
selected and the mean is found to be 23.2 years.
A. Find the 95% confidence interval for the population mean.
B. Find the 99% confidence interval for the population mean?
*in r studio file 4. The director of admissions of a small college selected 120 students...
*in r studio file
4. The director of admissions of a small college selected 120
students at random from the new freshman class in a study to
determine whether a student’s grade point average (GPA) at the end
of the freshman year (y) can be predicted from the ACT test score
(x). Estimate the simple linear regression of, y = β0 + β1x + ε,
using gpa.txt data and answer the following questions. (4
pts each)
(a) Report the least...
ADVERTISEMENT
ADVERTISEMENT
Latest Questions
- Write a program that computes the tax and tip on a restaurant bill for a patron...
- clear all close all % %*******Parameter Settings******** %********************************* Fs=8192; %Sampling frequency (MATLAB's default) Ts=1/Fs; %Sampling time...
- Name a business that you believe has experienced declining costs attributable to computerization. Were variable costs...
- With C++, 1. Assume we use two linked lists that represent Set A and Set B...
- A beam of light shines on an equilateral glass prism at an angle of 45∘ to...
- This is an intro to python question. #Write a function called search_for_string() that takes two #parameters,...
- C++ Give an example of overloading by implementing a function square(x), which calculates the square of...
ADVERTISEMENT