Do you ever think about the number of calories in your favorite foods?Explain.

Data Analysis
Do you ever think about the number of calories in your favorite foods? Maybe ice cream is better for you than a hamburger. One way to find out would be to figure out how many calories and grams of saturated fat are in both foods. Typically, foods have nutritional information like this on the packaging. Or if you eat out, many fast food places will provide this information. Once you have collected the data, you can begin to analyze it.

Create a perpendicular at point Q and label the intersection with the circle S. The length of this perpendicular is the square root of 6.

GEOMETRIC MEAN

You have learned how to construct a geometric mean with a compass and a straight edge- now we are going to put that knowledge into practice. For this example, we will utilize those techniques to construct a segment with a length of the square root of 6, when we are given a segment labeled PQ whose length is 6.

Recall that in a geometric mean problem, the means of the proportion must be the same. If we cross-multiply, we get x-squared equals a times b and x equals the square root of a b.

We know that we are looking for a segment that has the square root of 6 as its length. We can substitute the 6 into the last equation to get x equals the square root of 6. Squaring both sides gives us x-squared equals 6. Putting this information back into proportion form gives us 6 over x equals x over 1. Notice that we are not using 2 times 3 because the length of segment PQ is 6.

To make the construction we need to add the lengths of the extremes to have a single segment that is 7 units long and label it P R. Next, we will construct the perpendicular bisector of segment P R and use the point of intersection as the middle of our circle. Now, place the point of the compass on the intersection of our perpendicular and the segment P R. Extend the compass to either points P or R and draw the circle.

Lastly, we create a perpendicular at point Q and label the intersection with the circle S. The length of this perpendicular is the square root of 6. If we overlay the triangle P Q S, it is easy to see that the segment Q S is the geometric mean.

Provide a written description of the situation. Express the situation using the appropriate inequality and the correct units , if applicable.

Review the assigned reading to prepare for this discussion.

Linear inequalities come in one of the following basic forms:
a < x < b
x < b x > a
x < a or x > b
Note: The “< can be replaced with “≤” , and “>” can be replaced with “≥” in any of these cases, depending on the context of the problem or situation.

On a daily basis, you are likely to come across situations in which inequalities are alluded to without realizing the connection to math.

Example:
Perhaps you ordered furniture from a local department store and were given a delivery time window between 10 am and 2 pm on a certain day. This situation can be modeled using one of the four inequalities listed above. Additionally, the situation can be modeled graphically and with interval notation, as shown below.

Description: The furniture I ordered will be delivered between 10 am and 2 pm.
Inequality: 10am ≤ x ≤ 2pm
Interval notation:
Graph:

Inequality Graph with inequality 10am ≤ x ≤ 2pm and interval notation 10:00am, 2:00pm

Respond
Come up with a real-life situation that models each of the four types of inequalities listed above.
Provide a written description of the situation.
Express the situation using the appropriate inequality and the correct units , if applicable.
Express the situation using interval notation.

Is there a title that explains what the graph is displaying? Are numbers on the axis spaced out proportionally or have they been varied to create a dramatic impression?

Misleading Graphs

Initial Post Instructions

After exploring different types of graphs this week, it is unfortunate to learn that there are sometimes misleading graphs used in the news, politics, medicine, etc. in order to sway a decision or belief. Some items to watch out for in graphs are—

Is there a title that explains what the graph is displaying?
Are numbers on the axis spaced out proportionally or have they been varied to create a dramatic impression?
Is the graph too loud? Does it have too many components that it distracts from content?
Are there sources cited to know where the data came from?
Use the internet to find a misleading graph. Key Terms to Search: Misleading Graphs

Provide a screenshot of the graph
Cite the Source
Explain why the graph is misleading
Analysis

Explain how you would fix the graph so it is not misleading.
Explain why the creator of the misleading graph would want to create the graph in the first place.

What did you find interesting/surprising about the descriptive statistics in your peer’s post?

Descriptive Statistics
2020 unread replies.2626 replies.
Required Resources

Read/review the following resources for this activity:

Textbook: Chapter 1, 2
Lesson
Minimum of 1 scholarly source
Initial Post Instructions

When data is collected, the most common calculations computed are the Measures of Central Tendency, mean, median and mode. It is important to know how to compute these values and it is also extremely important to know what these values mean in context of the data set.

Use the internet to find a data set. Key terms to search: Free Public Data Sets and Medical Data Sets.

Introduce your Data Set and Cite the Source.
Why was this data interesting to you?
Calculate measures of central tendency and measures of variation for your data. Write a sentence for each calculation explaining what that value means in context of your data.
Follow-Up Post Instructions

Respond to at least one peer. Further the dialogue by providing more information and clarification.

Here are suggested responses.

What did you find interesting/surprising about the descriptive statistics in your peer’s post?
Complete a Compare/Contrast with your data set and a similar data set that was presented by a peer.

How many dollars does the person earn for that long day? $200

PARTICIPATION ACTIVITY
Piecewise linear function: Day’s earnings considering overtime pay.
Consider the example above.
1) Looking at the graph above, how much does a person earn for a day if the person worked 9 hours?
$80
$95
$100
2) No one line represents the function. To graph, the first piece’s line is:
0-8 hours: y = 10x
The second piece’s line starts at the first piece’s end, meaning x is 8 and y is 80. What is that line’s slope?
10
15
3) Drawing a line with slope 15, starting at x of 8 and y of 80, can be done by drawing a second point, obtained by going 1 unit to the right and up by how many units?

1
15
95
4) No one equation can represent the piecewise linear function. Instead, the function is described like this:
0-8 hours: y = 10x
8+ hours: y = 80 + 15(x – ?)

1
8
5) For more than 8 hours worked, the total earnings are y = 80 + 15(x – 8). A person works a long 20 hour day. How many dollars does the person earn for that long day?
$200
$260
$380
6) Suppose the company above pays double-time  for above 12 hours. The equations are then:
0-8 hours: y = 10x
8-12 hours: y = 80 + 15(x – 8)
12+ hours: y = ___ + 20(x – 12)
80
140
155
Feedback?
Overtime: Use and abuse

What is the overall savings for the no-phone contract after 24 months?What was the equation for the total cost of the with-phone contract?

Consider the example above.
1) What was the equation for the total cost of the with-phone contract?

Check Show answer
2) Shay chose to plot points for x = 10 and x = 20 because those values were round numbers and so a bit easier to calculate and draw. For the no-phone contract, what did Shay determine as the y value when x was 10?
$
Check Show answer
3) The graph of both contracts shows the with-phone contract to be how much cheaper at the start, when months is 0?
$
Check Show answer
4) The breakeven point, where the no-phone contract’s total cost becomes cheaper, is at how many months?
months
Check Show answer
5) The graphs not only show the breakeven point, but give a person a quick way to see the cost difference for any number of months. At 24 months, a person might visually see the blue line at about 1200 and the purple line at about 1000. What is the overall savings for the no-phone contract after 24 months?

Compare the t value in cell A29 to the table t value in cell A37. What is this comparison telling you about rejecting or not rejecting the null hypothesis. Put your explanation in cell A38.

One sample t Test
We are now going to use Excel to test a hypothesis based on one given sample. We would like to know if the average cholesterol level of patients in intensive care is equal to 200 and for that reason we collect cholesterol level of 20 random people from various intensive care units.
Cholesterol level
154,168,134,201,208,220,225,228,201,207,168,211,203,254,268,198,298,135,154,189

We put our data in column A. In Cells A3-A22 we type our data and in cell A1 we type Cholesterol.
First let’s input the sample size n, that is how many elements in data do we have. In cell B24 we type N and in cell A24 we type 20. Second, we find degrees of freedom df=N-1. In cell B25 we type df and in cell A25 we type =A24-1. Next we evaluate the mean. We learned that already. In cell B26 we type Mean and in cell A26 we type =average(A3:A22).
Now let’s do standard deviation. In cell B27 we type SD and in cell A27 we type =stdev(A3:A22).
Next let’s do standard error of the mean. In cell B28 we type SEM and in cell A28 we type =A27/sqrt(A24).
We will do a one sample t test and for that we need a t value. . In cell B29 we type t and in cell A29 we type =(A26-200)/A28.
Now we evaluate the p value using Excel. In cell B31 we type TEST value and in cell A31 we type 200 In cell B32 we type Mean Difference. In cell A32 we type =A26-A31 . In cell B33 we type Sig.(2-tailed). In cell A33 type =T.DIST.2T(A29,A25). Here T.DIST.2T means we are doing 2 tailed one sample TTEST. The first parameter A29 means we are computing the p value based on our calculated t value and we are comparing it to our threshold significance level of 0.05. The second variable represents degrees of freedom.
Exercises
Exercise 1. State the null hypothesis from this example in cell A35.
Exercise 2. What does the value in cell A33 tell you about the hypothesis. Do we reject the null hypothesis? Why? Put your explanation in cell A36.
Exercise 3. Instead of using Excel, we can look at the t chart. Find the critical value for the t distribution from that table. You may find it on page 335. Put that value in cell A37.
Exercise 4. Compare the t value in cell A29 to the table t value in cell A37. What is this comparison telling you about rejecting or not rejecting the null hypothesis. Put your explanation in cell A38.

Is the correlation evaluated in cell A15 positive or negative. Put your answer in cell A23.

Dependent groups t Test testing two mean differences
We are now going to use Excel to find information on correlation between two dependent groups. We would like to know if the cholesterol level depends on the age and for that reason we collect cholesterol level of 10 people, first when they were 17 and then when they are 46. We obtain this data
Cholesterol level at 17 Cholesterol level at 46
162 202
157 158
264 263
200 203
201 203
230 235
203 230
153 154
152 154
154 154

We put our data in columns A and B. In Cells A1-A10 we type our data for age 17 and in cell A11 we type Cholesterol at 17. In Cells B1-B10 we type our data for age 46 and in cell B11 we type Cholesterol at 46.
First let’s get the sample size n, that is how many pairs do we have. In cell B13 we type N and in cell A13 we type 10. Second, we find degrees of freedom df=N-1. In cell B14 we type df and in cell A14 we type =A13-1. Next we evaluate the correlation coefficient. We learned that already. In cell B15 we type Correlation R and in cell A15 we type =CORREL.
Now we evaluate the p value using Excel. In cell B16 we type Sig.(2-tailed). In cell A16 we type =TTEST . Here TTEST means we are doing TTEST. The first parameter A1:A10 means we are studying Cholesterol level at 17 and we are comparing it to the second variable B1:B10 which is Cholesterol level at 46. The third variable 2 means we are doing a 2 tail test. And the fourth variable being 1 means we are doing dependent groups. The fourth variable can also be 2 or 3. 2 would mean independent groups equal variance and 3 would mean independent groups not equal variance.
Now we find t value. In cell B17 we type t. In cell A17 we type =TINV(A16,A14).
We can find the table t value from the table or we can use Excel to find it. When we use Excel we type table t in cell B18. Then in cell A18 we type =TINV(.05,A14).

Exercises
Exercise 1. Is the correlation evaluated in cell A15 weak, moderate or strong. Put your answer in cell A22.
Exercise 2. Is the correlation evaluated in cell A15 positive or negative. Put your answer in cell A23.
Exercise 3. What does your result in cell A23 mean? Describe it in cell A24.
Exercise 4. The p value in cell A16 tells you something about a hypothesis. State the null hypothesis in cell A25.
Exercise 5. Look at the p value in cell A16. Does it mean that we reject the null hypothesis or that we do not reject it, and why. Put your answer in cell A26.
Exercise 6. Compare the t value in cell A17 to the table t value in cell A18. How does this comparison tell you if you should reject the null hypothesis or not. Put your explanation in cell A27.