The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 370 hours. Complete parts (a) through (d) below. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95% confidence interval estimate is from a lower limit of hours to an upper limit of hours. (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 420 hours? Explain. Based on the sample data, the manufacturer V the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is V standard errors V the sample mean, so it is V that the lightbulbs have a mean life of 420 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. O A. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O B. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. OC. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O D. No, since o is known and the sample size large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 77 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of hours to an upper limit of hours. (Round to one decimal place as needed.) Based on the sample data and a standard deviation of 77 hours, the manufacturer the right to state that the lightbullbs have a mean life of 420 hours. A mean of 420 hours is standard errors v the sample mean, so it is that the lightbulbs have a mean life of 420 hours.
The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 370 hours. Complete parts (a) through (d) below. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95% confidence interval estimate is from a lower limit of hours to an upper limit of hours. (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 420 hours? Explain. Based on the sample data, the manufacturer V the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is V standard errors V the sample mean, so it is V that the lightbulbs have a mean life of 420 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. O A. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O B. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. OC. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O D. No, since o is known and the sample size large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. d. Suppose the standard deviation changes to 77 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of hours to an upper limit of hours. (Round to one decimal place as needed.) Based on the sample data and a standard deviation of 77 hours, the manufacturer the right to state that the lightbullbs have a mean life of 420 hours. A mean of 420 hours is standard errors v the sample mean, so it is that the lightbulbs have a mean life of 420 hours.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:**Educational Website Content: Confidence Interval Estimation for Light Bulb Lifespan**
The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 370 hours. Complete parts (a) through (d) below.
**a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.**
The 95% confidence interval estimate is from a lower limit of \_\_ hours to an upper limit of \_\_ hours.
*(Round to one decimal place as needed.)*
**b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 420 hours? Explain.**
Based on the sample data, the manufacturer \_\_ the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is \_\_ standard errors \_\_ the sample mean, so it is \_\_ that the lightbulbs have a mean life of 420 hours.
**c. Must you assume that the population light bulb life is normally distributed? Explain.**
- ☐ A. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.
- ☐ B. No, since σ is known, the sampling distribution of the mean does not need to be approximately normally distributed.
- ☐ C. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.
- ☐ D. No, since σ is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.
**d. Suppose the standard deviation changes to 77 hours. What are your answers in (a) and (b)?**
The 95% confidence interval estimate would be from a lower limit of \_\_ hours to an upper limit of \_\_ hours.
*(Round to one decimal place as needed.)*
Based on the sample data and a standard deviation of 77 hours, the manufacturer \_\_ the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is \_\_ standard errors \_\_ the
Expert Solution
Step 1
Hey there! As per our policy we can answer only 3 sub-parts at a time. Please make a new request for remaining sub-part by mentioning the sub-parts that is needed.
Given data
Sample size(n) = 49
Sample mean x̅ = 370 hours
Population standard deviation = 98
Significance level(α) = 1-0.95 = 0.05
95% Confidence interval formula
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman