Question

A simple random sample of 60 items resulted in a sample mean of 84. The population standard deviation is 16. a. Compute the 95% confidence interval for the population mean (to 1 decimal). ( b. Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean (to 2 decimals). ( c. What is the effect of a larger sample size on the margin of error? Select Select It increases It decreases It stays the same It cannot be determined from the given data

Answer 1

Solution

given : = 84, o = 16, n = 60

for 95% confidence level, ze = 1.96

download link for excel to calculate za

https://drive.google.com/open?id=1jOoEZVCrBmmIf6nde0ODXC9dtT_Cr5CZ

$\dpi{100} \mathbf{formula:}\; Confidence\; interval\; for\; the \;population\; mean,\;\mu$

= 7+ Margin of error (E) Where, Margin of error (E) = 2*

${\color{Blue} \mathbf{(a)}}$

( 16 = 84 +1.96* 50* 1760/

= 444.0

= (84-4.0.84+4.0%

= (80.0.88.0)

(b) n = 120

_16 = 84 +1.96S 1120

= 442.9

= (84-2.9.84+29)

= (81.1.86.9%

(c) It decreases

The margin of error decreases as the sample size increases.