# A random, question on confidence intervals: 8:00 AM

edited February 18

(5 pts)

For this problem, you're going to compute a confidence interval for height based on some randomly generated data. Once you have your data and descriptive information, you'll compute your confidence interval in the form

$[bar{x} - z^** SE, bar{x} + z^** SE],$

where the $bar{x}$ is the mean of your sample and the standard error $SE = sigma//sqrt(n)$ is the standard deviation of your sample divided by the square root of the sample size. You should get your $z^**$-multiplier by using the calculator at the bottom of our normal calculator page.

You can get the specifics for your person question here.

• edited February 17

My data has 95 rows. The mean of my heights is 67.02 and the standard deviation is 4.43. I will use this information to compute a 90% confidence interval for height.

My SE is $SE = 4.43/(sqrt(95))$ and (from the calculator) my $z^**$-multiplier is $1.644854$. Thus, my confidence interval is:

$[67.02-(1.644854 times .45450841), 67.02+(1.644854 times .45450841)] = [66.2724, 67.766].$

• edited February 17

My data has 106 rows. The mean of my heights is 67.26 and the standard deviation is 4.84. I am using this information to compute a 90% confidence interval for height.

$overline x$ is $67.26$
SE is $4.84/(sqrt(106))$ or $.470102357381$
The $z$* multiplier is $1.644854$ from our confidence calculator

From this, my confidence interval is,
$[67.26−(1.6649)(.4701),67.26+(1.6649)(.4701)]$
which comes out to
$[66.47733051,68.04266949]$

• edited February 17

My data has 103 rows. The mean of your heights is 67.30 and the standard deviation is 4.75. I will use this information to compute a 94% confidence interval for height. My SE is found by
SE= $4.75/(sqrt (103))$

SE= .46807
z*= 1.880794

My Confidence interval is below.
[(67.30-(1.880794)(.46807), 67.30+(1.880794)(.46807)]

• edited February 17

My data has 104 rows. My mean is 66.77. My standard deviation comes to 4.22. I am computing for 91% confidence interval for height.

SE=$4.22/sqrt104$

z*=1.695398

With this information, the equation will look as follows...

$[66.77-(1.695348 ** 0.4138050451), 66.77+(1.695348 ** 0.4138050451)]=$

[66.06843575, 67.47156425]

• edited February 17

My data has 109 rows. The mean of my heights is 66.56 and the standard deviation is 3.59. I will use this information to compute a 91% confidence interval for height.
My SE is $SE = 3.59/sqrt(109)$
SE = 0.3438596364
Z* = 1.695398
My Confidence interval is below.
[66.56-(1.695398x.3438596364),66.56+(1.695398x.3438596364)] =
[65.97702106, 67.14297894]

• edited February 17

My data has 88 rows. The mean of my heights is 66.97 and the standard deviation is 4.90. I will use this information to compute a 98% confidence interval for height.

My SE is found by $SE= 4.90/(sqrt(88))$ therefore my SE= .5223417551 and (from the calculator) my z*- multiplier is 2.326348. Thus my confidence interval is

$[66.65-(2.326348)(.5223417551), 66.65+(2.326348)(.5223417551)=(65.732, 68.208) • edited February 17 I'm asked to compute a 92% confidence interval given a mean of 67.9, a standard deviation of 4.36, for a sample of size 98. Since my sample has size 98 and standard deviation 4.36, my standard error is:$SE = 4.35/sqrt(98) = 0.439416.$Using the calculator I find that my$z^$-multiplier is$z^
= 1.75.$Thus, my margin. of error is:$ME = z^** times SE = 1.75 times 0.439416 = 0.768978.$Finally, my confidence interval is:$[67.9 - 0.768978, 67.9 + 0.768978] = [67.131, 68.669].$• edited February 17 My data has 107 rows. The mean of my heights is 66.65 and the standard deviation is 4.30. I will use this information to compute a 98% confidence interval for height. My SE is$SE = 4.30/(sqrt(107)) =0.415696$and (from the calculator) my$z^*$-multiplier is$2.326348$. Thus my confidence interval is:$[66.65-(2.326348 times .415696), 66.65+(2.326348 times .415696)] = [65.6829, 67.6170].$• edited February 17 My data has 96 rows, the mean of my heights are 67.17 and the standard deviation is 4.09. I will compute a 95% confidence interval.$(4.09/(sqrt(96)))$SE= .417433877 z*= 1.960 My confidence interval is below [67.17-(.417433877)(1.960), 67.17+(.417433877)(1.960)= [66.341,67.999] • edited February 17 My data has 88 rows. The mean of my heights is 66.60 and the standard deviation is 4.09.$SE = 4.09/sqrt(88) = .435995$z* = 2.33 ME = z* times SE = 2.33 times .435995 = 1.01586835 My final confidence interval is: [66.60-1.01586835, 66.60+1.01586835] = [65.584,67.616] • My data has 101 rows. The mean of my heights is 67.13. The standard deviation is 4.55. I will compute a 94% confidence interval. 4.55/√101=.4527419215=SE z*=1.88 My confidence interval is below: [67.13-(.4527419215)(1.88), 67.13+(.4527419215)(1.88)= [66.279,67.980] • edited February 22 My data has 96 rows. The mean of your heights is 66.5 and the standard deviation is 4.38. I will use this information to compute a 97% confidence interval for height. My SE is found by$SE= 4.38/sqrt{96} =0.447$z*= 1.881 My Confidence interval is below.$[66.5-(1.881 * 4.38); 66.5+(1.881 * 4.38)] = [55.261,74.739]\$