A random sample of n measurements was selected from a population with unknown me

Question

A random sample of n measurements was selected from a population with unknown mean and standard deviation =35 for each of the situations in parts a through d. Calculate a 90% confidence interval for for each of these situations.

A random sample of n measurements was selected from a population with unknown mean mu and standard deviation omega = 35 for each of the situations in parts a through d. Calculate a 90% confidence interval for mu for each of these situations. a. n = 50, x = 24. b. n = 250, x = 106 c. n = 120, x = 17 d. n = 120, x = 4.06 e. Is the assumption that the underlying population of measurements normally distributed necessary (Round to two decimal places as needed.)

Explanation / Answer

a) The statistical software output for 90% confidence interval for the given data is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 35

90% confidence interval results:

Hence,

90% confidence interval will be:

(15.86, 32.14)

b) The statistical software output for 90% confidence interval for the given data is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 35

90% confidence interval results:

Hence,

90% confidence interval will be:

(102.36, 109.64)

c) The statistical software output for 90% confidence interval for the given data is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 35

90% confidence interval results:

Hence,

90% confidence interval will be:

(11.74, 22.26)

d) The statistical software output for 90% confidence interval for the given data is:

One sample Z confidence interval:
: Mean of population
Standard deviation = 35

90% confidence interval results:

Hence,

90% confidence interval will be:

(-1.20, 9.32)

e) No, because the sample size in all the cases are greater than 30.

Mean n Sample Mean Std. Err. L. Limit U. Limit 50 24 4.9497475 15.85839 32.14161

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