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

(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.

## Comments

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:

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

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 $67.26$

SEis $4.84/(sqrt(106))$ 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

$[66.47733051,68.04266949]$

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)]

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]

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]

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)

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= 1.75.$$z^

Thus, my margin. of error is:

$ME = z^** times SE = 1.75 times 0.439416 = 0.768978.$

Finally, my confidence interval is:

$[67.9 - 0.768978, 67.9 + 0.768978] = [67.131, 68.669].$

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:

$[66.65-(2.326348 times .415696), 66.65+(2.326348 times .415696)] = [65.6829, 67.6170].$

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]

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]

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.

$[66.5-(1.881 * 4.38); 66.5+(1.881 * 4.38)] = [55.261,74.739]$