A confidence interval for your CDC sample

(10 pts)

In this problem, you’re going to use our Data Explorer to help you write down a couple confidence intervals for height. To get started, download your data set after choosing your name from this list:

Once you have your data, upload it to our Data Explorer. Then, use that to find the mean, standard deviation, and sample size of your data. With that information,

• Find the standard error associated with your sample,
• Find the margin of error for a 95% level of confidence,
• Express your confidence interval in the form

• Do the same for a 99% level of confidence

My data had 110 individuals with a mean \bar{x} = 67.736 and a standard deviation s=4.176. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and myconfidence interval is

Here’s what I typed to produce this:

My data had 110 individuals with a mean $\bar{x} = 67.736$ and a standard deviation $s=4.176$. Therefore, my standard error is
$$
SE \approx s/\sqrt{n} = 4.176/\sqrt{110} = 0.398.
$$
For a 95% confidence interval, I need a $z^*$ multiplier of 2 to get
$$
ME = 2\times0.398 = 0.796.
$$
Thus, my confidence interval is
$$
[67.736 - 0.796, 67.736 + 0.796] = [66.94, 68.532].
$$
For a 99% level of confidence, the [normal calculator indicates that I need a $z^*$ multiplier of $2.576$. Thus, my margin of error is now
$$
ME = 2.576\times0.398 = 1.02525
$$
and myconfidence interval is
$$
[67.736 - 1.02525, 67.736 + 1.02525] = [66.7108, 68.7613].
$$

My data had 122 individuals with a mean \bar{x} = 67.62295081967213 and a standard deviation s=4.04995228795987. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and myconfidence interval is

My data had 111 individuals with a mean \bar{x} = 67.630 and a standard deviation s=3.849. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and myconfidence interval is

My data had 118 individuals with a mean \bar{x} = 67.407 and a standard deviation s=3.844. Therefore, my standard error is
SE \approx s/\sqrt{n} = 3.844/\sqrt{118} = 0.353.
For a 95% confidence interval, I need a z^* multiplier of 2 to get
ME = 2\times0.353 = 0.706.
Thus, my confidence interval is
[67.407 - 0.706, 67.407 + 0.706] = [66.701, 68.113].
For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now
ME = 2.576\times0.353 = 0.909
and myconfidence interval is
[67.407 - 0.909, 67.407 + 0.909] = [66.498, 68.316].

My data had 93 individuals with a mean \bar{x} = 66.89 and a standard deviation s=4.434. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and myconfidence interval is

My data had 103 individuals with a mean \bar{x} = 67.83495145631068 and a standard deviation s=4.2173709108378405. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.575829. Thus, my margin of error is now

and my confidence interval is

my data had 100 individuals. mean = 67.495 standard deviation = 3.764

SE = 3.764/10 = 0.3764
95% CONFIDENCE INTERVAL Z* OF 2 =
ME = 2X0.376 = 0.753
CONFIDENCE INTERVAL = {67.495 - 0.753,67.495+0.753} = {66.742, 67.248}
99% CONFIDENCE LEVEL Z* = 2.576
ME = 2.576 X 0.376 = 0.968
CONFIDENCE INTERVAL = {67.495-0.968,67.495+0.968} = {66.527, 68.463}

My data had 96 intervals with a mean of 67.364 and a standard deviation s= 4.255.
Therefore, my standard error is
SE= 4.176/ 96 = 0.434

For a 95% confidence level I need a z* multiplier of 2 to get

                                        ME= 2 x 0.434 = 0.868

Thus, my confidence interval is

                                   [67.364 - 0.868, 67.364 + 0.868] = [66.496, 68.232]

For a 99% level of confidence, the normal calculator indicates that I need a z* multiplier of 2.575. Thus my margin of error is now

                                  ME= 2.575 x 0.434 = 1.11755

and my confidence interval is

                                 [67.364 - 1.11755, 67.364 + 1.11755] = [66.24645, 68.48155]

My data had 95 individuals with a mean of 67.726 and a standard deviation s = 4.1242.

Therefore my standard error is 0.398

For a 95% confidence interval I have a ME of 0.796
So my confidence interval is [66.94, 68.5832]

For a 99% confidence interval I have a ME of 1.02525
So my confidence interval is [66.7108, 68.7613]

My data had 95 individuals with a mean \bar{x} = 67.72631578947369 and a standard deviation s=4.124246172934007. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and myconfidence interval is

My data had 98 individuals with a mean \bar{x} = 67.612 and a standard deviation s=4.017. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 2 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.576. Thus, my margin of error is now

and my confidence interval is

My data had 87 individuals with a mean \bar{x} = 67.1264 and a standard s = 4.1758

The standard error associated with my sample is; SE \approx s / \sqrt {n} = 4.1758 / \sqrt {87}= 0.44769
For a 95% confidence level my Margin of error is; ME = 2 \times 0.44769 = 0.895385

My confidence interval is; [67.1264- 0.895385, 67.1264+ 0.895385]=[66.2310, 68.0217]

For a 99% confidence level my Margin of error is now; ME= 2.576 \times 0.44769= 1.1552

As well as my confidence level is now; [67.1264- 1.1552, 67.1263+ 1.1552]= [65.9712, 68.2816]

Here’s what I typed to produce this:

My data had 111 individuals with a mean \bar{x} = 67.342 and a standard deviation s=4.137. Therefore, my standard error is

For a 95% confidence interval, I need a z^* multiplier of 1.76 to get

Thus, my confidence interval is

For a 99% level of confidence, the [normal calculator indicates that I need a z^* multiplier of 2.5758. Thus, my margin of error is now

and myconfidence interval is

My data set had 84 observations with a mean of 66.845, and a standard deviation of 4.309

for 95% confidence my SE =(4.309/9.165)=.470 ME = (.470*2) = .940 therefore my confidence interval is (66.845-.94,66.845+.94) = (65.905,67.785)

for a 99% confidence interval my z multiplier is 2.576
so (.470*2.756 =1.211) ME = 1.211 and my confidence interval is = (66.845-1.211,66.845+1.211) or = (65.634,68.056)