11)
Mean = 143
S.d = 35
When n = 35
As the population s.d is unknown we will use t distribution to estimate the interval
Degrees of freedom is = n-1 = 34
Critical value t from table for 34 degrees of freedom and 95% confidence level is = 2.03
Margin of error = t*s.d/√n = 2.03*35/√35 = 12.02
Required interval is
(Mean - MOE, Mean + MOE)
( 130.98, 155.02 )
Width = 155.02 - 130.98 = 24.04
When N =1000
Degrees of freedom is = n-1 = 999
For 999 df and 95% confidence level critical value t is = 1.96
Margin of error = 1.96*35/√1000 = 2.17
Interval is
(140.83, 145.17)
Width = 145.17 - 140.83 = 4.34
B)
As the sample size increases, width of the interval decreases
And also as the sample size increases, t distribution approaches to normal distribution
problem 11 10. Confidence Intervals Repeat Problem 9 using a confidence level of 95 % and...
Confidence Intervals 9. Construct a 95 % confidence interval for the population mean, . In a random sample of 32 computers, the mean repair cost was $143 with a sample standard deviation of $35 (Section 6.2) Margin of error, E. <με. Confidence Interval: O Suppose you did some research on repair costs for computers and found that the population standard deviation, a,- $35. Use the normal distribution to construct a 95% confidence interval the population mean, u. Compare the results....
problems 4, 5, 6, 11 and 13 If the population standard deviation was doubled to 10.4 and the level of confidence remained at 90%, what would be the new margin of error and confidence interval Margin of error, E. Confidence interval: 20.11<x<34.31 O Did the confidence interval increase or decrease and why? increase 4. Definition of Confidence Intervals (Section 6.1) Circle your answer, True of False. • A 99% confidence interval means that there is a 99% probability that the...
QUESTION 3 All things being equal, which is correct? As the confidence level increases, the margin of error gets larger. As the sample size increases, the confidence interval gets wider. As the standard deviation increases, the margin of error gets smaller. As the sample mean increases, the margin of error gets larger. Which of the following is correct? As the sample size increases, the confidence level decreases. As the confidence level increases, the width of the confidence interval decreases. As...
3. Complete the statements: The _______ of the confidence interval is exactly twice that of the _______ . When C increases from 90% to 98%, the width of the interval slightly_______ . When the interval increases, the precision_______ One way to reduce the margin of error is to increase the_______ 4. A random sample of the costs of repair jobs at a large muffler repair shop produces a mean of $127.95 and a standard deviation of $24.03. If the size of...
Find the margin of error for a 95% confidence interval for estimating the population mean when the sample standard deviation equals 92, with a sample size of (a) 400,(b) 1800. What is the effect of the sample size? 2. The margin of error for a 95% confidence interval with a sample size of 400 is (Round to the nearest tenth as needed.) b. The margin of error for a 90% confidence interval with a sample size of 1600 is (Round...
Determine the margin of error for a 95% confidence interval to estimate the population mean when s=37 for the sample sizes below. Solve for c) n=46. htmathe Student Homework Theme =41778etod y FALL 2019 STAT 3309 CRN 120961 Homework: Section 8.3 Confidence intervals with s Homework Score: 0 57 of 1 pt 28.3.22-T Determine the margin of error for a 95% confidence interval to estimate the E a) n. 13 b) n = 30 c) n46 a) The margin of...
Module 6: Problem 9 Previous Problem Problem List Next Problem (1 point) In the following questions, use the t-distribution to find a confidence interval for a difference in means #1 - Ma given the relevant sample results. Give the best point estimate for Hi-12, the margin of error, and the confidence interval. Assume the results come from random samples from a populations that are approximately normally distributed. Give your answers to 2 decimal places 1. A 80% interval for Mi...
to estimate the population mean repair cost of microwave ovens in macomb, a random sample of 9 broken microwave ovens was selected and it is found that the sample mean repair cost was $80 with a sample standard deviation of $15. 1) what would be the “critical value” if you want to find a 95% confidence interval for the population mean? 2) what would be the “margin of error” if you want to find a 95% confidence interval for the...
Assume a sample of 100 units provide a 95% confidence interval [10,20]. Which of the following is TRUE? Question 1 options: margin of error = 5, sample mean = 15 margin of error = 15, sample mean = 5 margin of error = 10, sample mean = 15 margin of error = 15, sample mean = 30 Question 2 (1 point) Assume a sample of 100 units provide a 95% confidence interval [10,20]. Which of the following could correspond to...
Confidence Interval Given. Assume I created a 95% confidence interval for the mean hours studied for a test based on a random sample of 64 students. The lower bound of this interval was 4 and the upper bound was 14. Assume that when I created this interval I knew the population standard deviation. Using this information, (a) Calculate the width of the interval. (b) Calculate the margin of error for the interval. (c) Calculate the center of the interval. (d)...