A simple random sample of size n is drawn. The sample mean , x is found to be 18
ID: 3130098 • Letter: A
Question
A simple random sample of size n is drawn. The sample mean , x is found to be 18.5 and the sample standard deviation ,s, is found to be 48.
Construct a 95% confidence interval about u if the sample size, n, is 34. lower bound_____: upper bound______
(b) Construct a 95% confidence interval about u if the sample size n 61. Lower bound____; upper bound______
how does increasing the sample size affect the margin of error? (A) the margin of error decrease (B) the margin of error does (C)
construct a 99% confidence interval about u if the sample size, n, is 34. lower bound____; upper bound_____
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error? (A) the margin of error does not change (B) the margin of error increases (C) the margin of error decreases
(d) if the sample size is 15, what conditions must be satisfied to compute the confidence interval
(A) the sample must come from a population that is normally distributed and the sample size must be large (B) the data must come from a population that is normally distributed with no outliers (C) The sample size must be large and the sample should not have any outliers
Explanation / Answer
A simple random sample of size n is drawn. The sample mean , x is found to be 18.5 and the sample standard deviation ,s, is found to be 48.
Construct a 95% confidence interval about u if the sample size, n, is 34. lower bound 1.75: upper bound 35.25
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
48
Sample Mean
18.5
Sample Size
34
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
8.231932087
Degrees of Freedom
33
t Value
2.0345
Interval Half Width
16.7480
Confidence Interval
Interval Lower Limit
1.75
Interval Upper Limit
35.25
(b) Construct a 95% confidence interval about u if the sample size n 61. Lower bound 6.21; upper bound 30.79
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
48
Sample Mean
18.5
Sample Size
61
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
6.145770237
Degrees of Freedom
60
t Value
2.0003
Interval Half Width
12.2934
Confidence Interval
Interval Lower Limit
6.21
Interval Upper Limit
30.79
how does increasing the sample size affect the margin of error?
(A) the margin of error decrease
(B) the margin of error does not change
(C)
construct a 99% confidence interval about u if the sample size, n, is 34. lower bound -4.0; upper bound 41.0
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
48
Sample Mean
18.5
Sample Size
34
Confidence Level
99%
Intermediate Calculations
Standard Error of the Mean
8.231932087
Degrees of Freedom
33
t Value
2.7333
Interval Half Width
22.5001
Confidence Interval
Interval Lower Limit
-4.00
Interval Upper Limit
41.00
Compare the results to those obtained in part (a). How does increasing the level of confidence affect the size of the margin of error?
(A) the margin of error does not change
(B) the margin of error increases
(C) the margin of error decreases
(d) if the sample size is 15, what conditions must be satisfied to compute the confidence interval
(A) the sample must come from a population that is normally distributed and the sample size must be large
(B) the data must come from a population that is normally distributed with no outliers
(C) The sample size must be large and the sample should not have any outliers
Confidence Interval Estimate for the Mean
Data
Sample Standard Deviation
48
Sample Mean
18.5
Sample Size
34
Confidence Level
95%
Intermediate Calculations
Standard Error of the Mean
8.231932087
Degrees of Freedom
33
t Value
2.0345
Interval Half Width
16.7480
Confidence Interval
Interval Lower Limit
1.75
Interval Upper Limit
35.25
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