Answer:
It is an octogan and it isn't regular, you are correct.
Step-by-step explanation:
Normal octagons look like a stop sign. This one looks like a star.
Here is the correct question.
The manufacturer of a smart watch claims that individuals who pay attention to how many steps they take per day will inadvertently take more steps per day than individuals who pay no attention to how many steps they take per day. To investigate this claim, the manufacturer conducts a study to estimate the difference in the mean number of steps taken by those that pay attention to how many steps they take per day and those that do not. To do so, 40 volunteers are recruited. Half of the volunteers are randomly assigned to receive a smart watch and are taught how to use it to track their steps. The other half of the volunteers are given a wristband to wear, but are not informed that the wristband is tracking their steps. The volunteers are monitored for 30 days. The mean and standard deviation of the number of steps taken per day are computed for each group. Here are the data:
![S_x](https://tex.z-dn.net/?f=S_x)
Pay attention 20 10,244 1,580
Do not pay attention 20 8.,648 2,350
Which of the following is a 99% confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 ?
Answer:
![\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28A%29%20%20%5C%201596%20%20%5C%20%5Cpm%202.861%20%5Csqrt%7B%20%5Cdfrac%7B1580%5E2%7D%7B20%7D%20%2B%20%5Cdfrac%7B2350%5E2%7D%7B20%7D%7D%7D)
Step-by-step explanation:
Given that :
significance level ![\alpha = \mathbf{0.01}](https://tex.z-dn.net/?f=%5Calpha%20%3D%20%5Cmathbf%7B0.01%7D)
From the Given data;
Using Excel with the function : TINV(0.01,19);
Critical value t* = 2.861
The margin of error can now be represented by the illustration:
Margin of error = ![t^* \sqrt{ \dfrac {s_1 ^2}{n_1} + \dfrac {s_2 ^2}{n_2}](https://tex.z-dn.net/?f=t%5E%2A%20%5Csqrt%7B%20%5Cdfrac%20%7Bs_1%20%5E2%7D%7Bn_1%7D%20%2B%20%5Cdfrac%20%7Bs_2%20%5E2%7D%7Bn_2%7D)
Lower Limit = ![(\bar x_1 - \bar x_2)- (Margin \ of \ error)](https://tex.z-dn.net/?f=%28%5Cbar%20x_1%20-%20%5Cbar%20x_2%29-%20%28Margin%20%5C%20of%20%5C%20error%29)
Upper Limit = ![(\bar x_1 - \bar x_2)+ (Margin \ of \ error)](https://tex.z-dn.net/?f=%28%5Cbar%20x_1%20-%20%5Cbar%20x_2%29%2B%20%28Margin%20%5C%20of%20%5C%20error%29)
Thus; the confidence interval for the difference in the mean number of steps taken by all people like these that do and do not pay attention to the number of steps they take per day using df - 19 is:
![\mathbf{(A) \ 1596 \ \pm 2.861 \sqrt{ \dfrac{1580^2}{20} + \dfrac{2350^2}{20}}}](https://tex.z-dn.net/?f=%5Cmathbf%7B%28A%29%20%20%5C%201596%20%20%5C%20%5Cpm%202.861%20%5Csqrt%7B%20%5Cdfrac%7B1580%5E2%7D%7B20%7D%20%2B%20%5Cdfrac%7B2350%5E2%7D%7B20%7D%7D%7D)
The approximations of the mean and the standard deviation are 233.3 and 229.82, respectively
<h3>How to determine the mean?</h3>
The table of values is given as:
Savings Lower Limit Upper Limit Frequency
0-199 0 199 345
200-399 200 399 97
400-599 400 599 52
600-799 600 799 21
800-999 800 999 9
1000-1199 1000 1199 8
1200-1399 1200 1399 3
Rewrite the table to include the class midpoint and the frequency
x f
99.5 345
299.5 97
499.5 52
699.5 21
899.5 9
1099.5 8
1299.5 3
The mean is calculated as:
![\bar x = \frac{\sum fx}{\sum f}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B%5Csum%20fx%7D%7B%5Csum%20f%7D)
So, we have:
![\bar x = \frac{99.5* 345 + 299.5* 97 + 499.5* 52 + 699.5 * 21 + 899.5 * 9 + 1099.5 * 8 + 1299.5 * 3}{345 + 97 + 52 + 21 + 9 + 8 +3}](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20%5Cfrac%7B99.5%2A%20345%20%2B%20299.5%2A%2097%20%2B%20499.5%2A%2052%20%2B%20699.5%20%2A%2021%20%2B%20899.5%20%2A%209%20%2B%20%201099.5%20%2A%208%20%2B%201299.5%20%2A%203%7D%7B345%20%2B%2097%20%2B%2052%20%2B%2021%20%2B%209%20%2B%208%20%2B3%7D)
Evaluate
![\bar x = 233.331775701](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20233.331775701)
Approximate
![\bar x = 233.3](https://tex.z-dn.net/?f=%5Cbar%20x%20%3D%20233.3)
Hence, the approximation of the mean is 233.3
<h3>How to determine the standard deviation?</h3>
The standard deviation is calculated as:
![\sigma = \sqrt{\frac{\sum f(x - \bar x)^2}{\sum f}}](https://tex.z-dn.net/?f=%5Csigma%20%3D%20%5Csqrt%7B%5Cfrac%7B%5Csum%20f%28x%20-%20%5Cbar%20x%29%5E2%7D%7B%5Csum%20f%7D%7D)
So, we have:
![\sigma= \sqrt{\frac{(99.5-233.3)^2* 345 + (299.5-233.3)^2* 97 +...... + (1299.5 -233.3)^2* 3}{345 + 97 + 52 + 21 + 9 + 8 +3}](https://tex.z-dn.net/?f=%5Csigma%3D%20%5Csqrt%7B%5Cfrac%7B%2899.5-233.3%29%5E2%2A%20345%20%2B%20%28299.5-233.3%29%5E2%2A%2097%20%2B......%20%2B%20%281299.5%20-233.3%29%5E2%2A%203%7D%7B345%20%2B%2097%20%2B%2052%20%2B%2021%20%2B%209%20%2B%208%20%2B3%7D)
Evaluate
![\sigma = 229.82](https://tex.z-dn.net/?f=%5Csigma%20%3D%20229.82)
Hence, the approximation of the standard deviation is 229.82
Read more about mean and standard deviation at:
brainly.com/question/475676
#SPJ1
The answer is C. "6 1/4" :)