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MTH 250 – PROJECT Due by 5/11/2021

Please answer all of the following questions. Be neat, show your work, use full sentences and explain

your answers. Please professionally present your project. Use Excel to create your graphs.

You can work with a partner if you want. If you plan to work with a partner, you must let me know at

least a week before the project’s due date. If you work with a partner, you can turn in just one

project.

Please do your own work, and do not copy anyone else’s project. If you have trouble obtaining the data,

let me know.

PART 1: M&M’s

For this part of the project, you will need to obtain a bag of M&Ms and count how many M&Ms there

are of each color. (If you don’t want to do M&Ms you could do Skittles, or count how many of each type of nut are in a

container of mixed nuts. If you have another similar idea that you would like to do, let me know so I can approve it)

1. What is the variable we are studying? Is this variable quantitative or qualitative? If the variable

is quantitative, is it continuous or discrete?

2. Create a frequency distribution for the number of M&M’s of each color.

3. Create a relative frequency distribution for the number of M&M’s of each color.

4. What is the mode?

5. Create a graph to display this data. Make sure your graph is labeled appropriately. (You can

select the type of graph you think is appropriate)

PART 2: Cereal

For this part of the project, you should go to the grocery store (or online store..) and look at the

nutrition facts for many different boxes of cereal. I would recommend collecting data on at least 20

types of cereal.

For each cereal please make a table of the following data:

(If the cereal lists nutrition information for being served with milk, please just use the nutrition information for plain cereal.)

Name of Cereal Grams of Total Carbohydrates Grams of Fiber

Please include the table with your project.

For each of these two variables:

1. Is the variable qualitative or quantitative? If the variable is quantitative, is it continuous or

discrete?

2. Find the mean, median, sample standard deviation, and IQR. Find the five-number summary.

3. Calculate whether there are any outliers. If there are outliers, explain how you could tell these

values are outliers. If there are no outliers, explain how you decided there are no outliers.

4. Create a histogram. (You can group data in classes) Make sure your graph is labeled

appropriately.

5. Create a boxplot.

6. Looking at the histogram and/or boxplot, what shape would you say that the data has? (If the

shape is kind of awkward, that’s okay. Give your best analysis of it.)

7. If you had to report on the typical amount of carbohydrates and the typical amount of fiber in

a serving of cereal, what measure of the center would you use for each one? Why?

Two more problems:

8. A high-fiber cereal boasts that it contains 20 g of fiber. A low-carb cereal has just 14g of

carbohydrates. Use the means and standard deviations you calculated to find a z-score for each

cereal of these cereals. Based on these z-scores, which cereal is more exceptional?

9. For this problem, choose whichever of the variables was approximately bell-shaped.

If both were bell-shaped, choose either one; If neither one is bell-shaped choose the closest one to bell-shaped and we will pretend it was bell-shaped.

Use empirical rule to state the values that approximately 68%, 95%, and 99.7% of cereals

would fall between.

Part III: Confidence Interval

This part of your project will be to construct confidence intervals and perform hypothesis tests without using the

calculator to do all the work. Also, you must be able to interpret your results. Please round answers to 3 decimal

places.

Not Allowed: Do not use anything in the STAT > > TESTS menu Allowed: You can use 1-Var Stats.

10. Confidence Interval

In a study of maximal aerobic capacity, 12 women had their blood plasma volume measured. The following

data is their blood plasma volumes in liters.

3.75 2.89 2.70 3.12 2.61 3.85

2.96 3.87 3.15 2.96 3.52 3.12

a. Calculate the mean and sample standard deviation of the women’s blood plasma volume. (You can

use 1-Var Stats on your calculator)

b. We want to find a 90% confidence interval. What is the critical value 𝒕𝜶/𝟐? Explain how you found it.

c. Construct a 90% confidence interval for the mean women’s blood plasma volume by using the

formula. Show your work.

d. Write a sentence to interpret the confidence interval that you constructed.

e. We would like to redo this study with better accuracy. We would like the margin of error to be no

more than 0.1 liters. What sample size should we use for our new study?

Part IV: Hypothesis

11. Hypothesis Test

The ToothBright Toothpaste Company claims that 4 out of 5 dentists (80% of dentists) recommend their

toothpaste to patients. You think that the proportion of dentists who recommend ToothBright is less

than that, so you contact 100 randomly selected dentists across the country to ask if they recommend

ToothBright toothpaste to their patients, and 71 of them said yes.

Perform your hypothesis test at the α=.05 level of significance.

a. State the null and alternative hypotheses.

b. Calculate the test statistic. Show your work.

c. What is the correct critical value (or values) for the problem? Explain how you found it.

d. Mark the Critical Value(s) and the Test Statistic on the curve. Also, indicate clearly which area is

the critical region.

e. Is your test statistic in the critical region?

f. Are you going to reject or fail to reject the null hypothesis? How did you decide?

g. State your conclusion. (without using words like “reject” and “hypothesis”)

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Unformatted Attachment Preview

MTH 250 – PROJECT

Due by 5/11/2021

Please answer all of the following questions. Be neat, show your work, use full sentences and explain

your answers. Please present your project in a professional way. Use Excel to create you graphs.

You can work with a partner if you want. If you plan to work with a partner, you must let me know at

least a week in advance of the project due date. If you work with a partner, you can turn in just one

project.

Please do your own work, and do not copy anyone else’s project. If you have trouble obtaining the data,

let me know.

PART 1 : M&M’s

For this part of the project you will need to obtain a bag of M&Ms and count how many M&Ms there

are of each color. (If you don’t want to do M&Ms you could do Skittles, or count how many of each type of nut are in a

container of mixed nuts. If you have another similar idea that you would like to do, let me know so I can approve it)

1. What is the variable we are studying? Is this variable quantitative or qualitative? If the variable

is quantitative, is it continuous or discrete?

2. Create a frequency distribution for the number of M&M’s of each color.

3. Create a relative frequency distribution for the number of M&M’s of each color.

4. What is the mode?

5. Create a graph to display this data. Make sure your graph is labeled appropriately. (You can

select the type of graph you think is appropriate)

PART 2 : Cereal

For this part of the project you should go to the grocery store (or online store..) and look at the

nutrition facts for many different boxes of cereal. I would recommend collecting data on at least 20

types of cereal.

For each cereal please make a table of the following data:

(If the cereal lists nutrition information for being served with milk, please just use the nutrition information for plain cereal.)

Name of Cereal

Grams of Total Carbohydrates

Please include the table with your project.

For each of these two variables:

Grams of Fiber

1. Is the variable qualitative or quantitative? If the variable is quantitative, is it continuous or

discrete?

2. Find the mean, median, sample standard deviation, and IQR. Find the five number summary.

3. Calculate whether there are any outliers. If there are outliers, explain how you could tell these

values are outliers. If there are no outliers, explain how you decided there are no outliers.

4. Create a histogram. (You can group data in classes) Make sure your graph is labeled

appropriately.

5. Create a boxplot.

6. Looking at the histogram and/or boxplot, what shape would you say that the data has? (If the

shape is kind of awkward, that’s okay. Give your best analysis of it.)

7. If you had to report on the typical amount of carbohydrates and the typical amount of fiber in

a serving of cereal, what measure of center would you use for each one? Why?

Two more problems:

8. A high-fiber cereal boasts that it contains 20 g of fiber. A low-carb cereal has just 14g of

carbohydrates. Use the means and standard deviations you calculated to find a z-score for each

cereal of these cereals. Based on these z-scores, which cereal is more exceptional?

9. For this problem, choose whichever of the variables was approximately bell-shaped.

If both were bell-shaped, choose either one; If neither one is bell-shaped choose the one that was closest

to bell-shaped and we will pretend it was bell-shaped.

Use empirical rule to state the values that approximately 68%, 95%, and 99.7% of cereals

would fall between.

Part III: Confidence Interval

This part of your project will be to construct confidence intervals and perform hypothesis tests without using the

calculator to do all the work. Also, you must be able to interpret your results. Please round answers to 3 decimal

places.

Not Allowed: Do not use anything in the STAT > > TESTS menu

10.

Confidence Interval

Allowed: You can use 1-Var Stats.

In a study of maximal aerobic capacity, 12 women had their blood plasma volume measured. The following

data is their blood plasma volumes in liters.

3.75

2.96

2.89

3.87

2.70

3.15

3.12

2.96

2.61

3.52

3.85

3.12

a. Calculate the mean and sample standard deviation of the women’s blood plasma volume. (You can

use 1-Var Stats on your calculator)

b. We want to find a 90% confidence interval. What is the critical value 𝒕𝜶/𝟐 ? Explain how you found it.

c. Construct a 90% confidence interval for the mean women’s blood plasma volume by using the

formula. Show your work.

d. Write a sentence to interpret the confidence interval that you constructed.

e. We would like to redo this study with better accuracy. We would like the margin of error to be no

more than 0.1 liters. What sample size should we use for our new study?

Part IV: Hypothesis

11. Hypothesis Test

The ToothBright Toothpaste Company claims that 4 out of 5 dentists (80% of dentists) recommend their

toothpaste to patients. You think that the proportion of dentists who recommend ToothBright is less

than that, so you contact 100 randomly selected dentists across the country to ask if they recommend

ToothBright toothpaste to their patients, and 71 of them said yes.

Perform your hypothesis test at the α=.05 level of significance.

a. State the null and alternative hypotheses.

b. Calculate the test statistic. Show your work.

c. What is the correct critical value (or values) for the problem? Explain how you found it.

d. Mark the Critical Value(s) and the Test Statistic on the curve. Also indicate clearly which area is

the critical region.

e. Is your test statistic in the critical region?

f.

Are you going to reject or fail to reject the null hypothesis? How did you decide?

g. State your conclusion. (without using words like “reject” and “hypothesis”)

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Tags:

null hypothesis

z test

frequency distribution

test statistic

alternative hypotheses

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