Question
In: Math
You may need to use the appropriate appendix table or technology to answer this question. A...
You may need to use the appropriate appendix table or technology to answer this question.
A 95% confidence interval for a population mean was reported to be 151.29 to 160.71. If
σ = 15,
what sample size was used in this study? (Round your answer to the nearest integer.)
Solutions
Expert Solution
Solution :
Given that,
Lower confidence interval = 151.29
Upper confidence interval =160.71
=
(Lower confidence interval + Upper confidence interval ) / 2
= (151.29 +160.71) / 2
= 312 / 2
= 156
= 156
Margin of error =E = Upper confidence interval -
= 160.71- 156
= 4.71
Margin of error = 4.71
standard deviation = 
= 15
margin of error = E = 4.71
At 95% confidence level the z is ,
= 1 - 95% = 1 - 0.95 = 0.05
/ 2 = 0.05 / 2 = 0.025
Z/2
= Z0.025 = 1.960
Sample size = n = ((Z/2
*
) / E)2
= ((1.960 * 15) / 4.71)2
= 38.95
= 39
Sample size = 39
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