Question

A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is 15.

At 95% confidence, what is the margin of error (to 4 decimals)?

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What is the standard error of the mean (to 4 decimals)?

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Which statement should you use to explain the 95% confidence interval ?

Group of answer choices:

A. We are confident that 95% of population are in the confidence interval

B. We are 95% confident that the confidence interval includes the sample mean.

C. We are 95% confident that the confidence interval includes the population.

D. There is a 95% probability that the population mean lies within the confidence interval.

Answer 1

olution :

Given that,

Point estimate = sample mean = = 80

Population standard deviation =    = 15

Sample size = n = 60

A) At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

E = 1.96 * ( 15 /  60 )

E = 3.7955

B) = / n = 15 / 60 = 1.9365

At 95% confidence interval estimate of the population mean is,

  ± E

80 ± 3.7955   

( 76.2045, 83.7955 )  

C. We are 95% confident that the confidence interval includes the population.