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A shoe store wants to estimate the average shoe size of their customers. It is assumed that the shoe size of their customers follows a normal distribution. It is known from previous experience that the standard deviation of shoe size is 2.4 inches. They take a sample of 40 customers and obtains the average shoe size of 10.3 inches from them. Estimate a 97% confidence interval for the population mean. 10.3 +/- A company that sells pens knows that the number of days those pens last when used in an office is normally distributed with a standard deviation of 5 days. How many pens do they need to sample if they want to create a 95% confidence interval of the average number of days, with an error of +/- 2?

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Introductory Statistics
OER Edition, 2013
Openstax
ISBN: 9781938168208

Related questions

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.

 

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.
( ,  )

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.
 

. SAT scores are distributed with a mean of 1,500 and a standard deviation of 300. You are interested in estimating the average SAT score of first-year students at your college. If you would like to limit the margin of error of your 95% confidence interval to 25 points, how many students should you sample? Make sure to give a whole number answer

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Give your answers as decimals, to three places.

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