Question

Hand calculate , showing all work, 95% and 99% confidence intervals for μ and σ. and use the TI to obtain each output with this data 0, 0, 15, 15, 16, 18, 20, 20, 20, 25, 25, 30, 30, 30, 32, 32, 33, 33, 35, 35, 35, 35, 36, 36, 38, 38, 39, 39, 40, 40, 40

yes/no data:

out of 31, 27 said yes and 3 said no

Hand calculate, showing all work, 95% and 99% confidence intervals for p. and use the TI to obtain each output.

Answer 1

	X	X2
	0	0
	0	0
	15	225
	15	225
	16	256
	18	324
	20	400
	20	400
	20	400
	25	625
	25	625
	30	900
	30	900
	30	900
	32	1024
	32	1024
	33	1089
	33	1089
	35	1225
	35	1225
	35	1225
	35	1225
	36	1296
	36	1296
	38	1444
	38	1444
	39	1521
	39	1521
	40	1600
	40	1600
	40	1600
sum	880	28628
n	31
Mean	28.39

Here,

Number of observations (n) = 31

Sum of the observations = 880

  

  

  

1)

From Z-score table , Z value for 95% confidence interval = 1.96 and Z value for 99% confidence interval = 2.576

Now

95% confidence intervals for μ is given as

  

,

( 24.51 , 32.27 )

Therefore, 95% confidence intervals for μ is ( 24.51 , 32.27 )

99% confidence intervals for μ is given as

,

( 23.29 , 33.49 )

Therefore 99% confidence intervals for μ is ( 23.29 , 33.49 )

Finding confidence interval for :

Here,

n= 31

For 95% confidence interval ( )

95% confidence interval for is given as

For 99% confidence interval ( )

99% confidence interval for is given as

2)

Estimate of population proportion ( ) = 27 / 31 = 0.87

n = 31

Margin of Error is given by

For 95% confidence interval Z = 1.96

95% confidence interval for p is

,

,

( 0.7516 , 0.9884 )

And

For 99% confidence interval Z = 2.576

99% confidence interval for p is

,

,

( 0.7144 , 1.0256 )