Question

1.You are to construct a 97% confidence interval. The population is normally distributed and the "population standard deviation" is known to be 42. You will take a random sample of size 38. The margin of errors is = Please enter your response rounded to TWO places of decimal at the final step of the calculation.

2.You are to construct a 90% confidence interval for the mean of a normally distributed population. The population standard deviation is unknown. The sample standard deviation from a random sample was found to be 34; the sample size was 31. The margin of error, e = (Round your response entry to TWO places of decimal at the end of final calculation)

Answer 1

Solution :

Given that,

1) Population standard deviation =    = 42

Sample size = n = 38

At 97% confidence level

= 1 - 97%  

= 1 - 0.97 =0.03

/2 = 0.015

Z/2 = Z0.015 = 2.17

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

= 2.17 * ( 42 /  38 )

= 14.78

2) sample standard deviation = s = 34

sample size = n = 31

Degrees of freedom = df = n - 1 = 31 - 1 = 30

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,30 = 1.697

Margin of error = E = t/2,df * (s /n)

= 1.697 * (34 / 31)

Margin of error = E = 10.36