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Suppose a random sample of size 10 was taken from a normally distributed population, and the sample standard deviation was calculated to be s = 5.2.

 

a)  Calculate the margin of error for a 95% confidence interval for the population mean.

 

Give your response to at least 3 decimal places.

   

 

 

b)  Calculate the margin of error for a 90% confidence interval for the population mean.

 

Give your response to at least 3 decimal places.

 

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Priyanshu Patel
Priyanshu PatelLv10
12 Feb 2021
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Related textbook solutions

Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is 15 .

a. Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
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b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
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c. What is the effect of a larger sample size on the interval estimate?

Larger sample provides a  margin of error.
 

A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample mean, x¯\bar{x}ˉ, is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9. (a) Construct the 90% confidence interval for the population mean if the sample size, n, is 15. (b) Construct the 90% confidence interval for the population mean if the sample size, n, is 25. How does increasing the sample size affect the width of the interval? (c) Construct the 95% confidence interval for the population mean if the sample size, n, is 15. Compare the results to those obtained in part (a). How does increasing the level of confidence affect the confidence interval? (d) Construct the 90% confidence interval for the population standard deviation if the sample size, n, is 15.

 

1. A sample of size n=49 is drawn from a population whose standard deviation is .

(a) Find the margin of error for a 95%confidence interval for .

b) If the sample size were n=60, would the margin of error be larger would be larger or smaller.

2.  Determine the point estimate of the population mean and margin of error for the confidence interval. The lower bound is 23; the upper bound is 27. The point estimate of the population mean is? The margin of error for the confidence interval is?

 

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