Question

A population is believed to have a standard deviation of 16.7. A sample of size 68 is taken and the sample mean is calculated as 550.3. What is the margin of error (E) for a 90% confidence interval for the mean? Enter your answer to 2 decimal places.

A sample of size 6 is taken from a population with an unknown variance. The sample mean is 603.3 and the sample standard deviation is 189.8. Calculate a 95% confidence interval. What is the upper limit of the interval? Enter your answer to 1 decimal places.

A sample of size 67 is taken from a population with an unknown variance. The sample mean is 91.8 and the sample standard deviation is 6.7. Calculate a 95% confidence interval. What is the upper limit of the interval? Enter your answer to 1 decimal places.

A t-test on the mean of a population is performed with a sample of size 26 to generate a 90% confidence interval, what is the t value that should be used? Enter your answer to 3 decimal places.

Answer 1

a)

=16.7, n= 68,   = 550.3. c = 90%

formula for margin of error is

Where Zc is the z critical value for c= 90%

Zc= 1.645

= 3.3314

Margin of error ( E) =3.33

b)

n= 6, = 603.3, s= 189.8, c= 95%

formula for confidence interval is

now using t table calculate t critical value with df = n-1 = 5

we get,

tc =2.571

404.117 < < 802.483

upper limit =  802.5

c)

n= 67, = 91.8, s= 6.7, c= 95%

formula for confidence interval is

now using t table calculate t critical value with df = n-1 = 5

we get,

tc =1.997

90.166 < < 93.434

upper limit = 93.4

d) n= 26, c=90%,

now using t table calculate t critical value with df = n-1 = 25

we get,

Critical t value = 1.708