Math 1635 Statistics Probability (Chapter 4) Worksheet

1. If there are 20 marbles marked from 1 to 20 in the bag, what is the probability to pick a marble from the bag and the number can be

(a) divided by 2 or 5

(b) divided by 3 or 7

2. When a card is selected from the deck of 52 cards, find the probability of getting

(a) a spade or a face

(b) a queen or black

(c) a club or an 8

3. When 2 dice are rolled, find the probability of getting

(a) A sum of 7

(b) A sum greater than 8.

(c) A sum less than or equal to 5.

4. A bag contains 2 red, 3 green and 5 white balls. A ball is selected at random and its color is noted. Then it is replaced and another ball is selected and its color is noted. Find the probability of:

(a) selecting 2 green balls

(b) selecting red and then green balls

Two discussion groups are organized by randomly selected employees from each division. During the talks, the director lays out his marketing vision and employees ask questions relevant to their daily work. At the end, each employee has to rate the director on a scale from 1 to 10 (1=very bad; 10=very good). The HR department wants to know if the distribution of ratings of the marketing development employees is different among the employees of the two divisions.

a) Examine the distributions of the ratings (show histograms) by the two groups of employees and explain why a non-parametric test is justified to perform the analysis.

b) Perform an appropriate non-parametric test using a 5% significance level to determine if the distribution of ratings of the marketing development employees is different than that of the marketing operations employees. Specify any assumptions and/or conditions you need to make to apply the test and state your hypothesis clearly. Show your manual calculations.

c) Use Minitab to perform the test in b) above and compare your results

For this activity, you will be creating a confidence interval for the average number of hours of TV watched. Last semester, my MAT 152 online students asked the question, “How many hours of screen time do you have in a typical week?” Please use the data they collected to answer the following questions. Data: 21, 2, 28, 30, 18, 21, 25, 20, 25, 14, 21, 25, 50, 39, 46, 20, 35, 45, 37, 46 Are there any outliers in this data set? What calculator test (1-PropZInt, Z-Interval, or T-Interval), Excel, or StatCrunch function will you use to find the confidence interval? Why do you use this test (and not one of the other 2 tests)?

Here is the full question:

lease use the skills you learned in section 9.2 for this assignment.

For this activity, you will be creating a confidence interval for the average number of hours of TV watched. Last semester, my MAT 152 online students asked the question, “How many hours of screen time do you have in a typical week?” Please use the data they collected to answer the following questions.

Data: 21, 2, 28, 30, 18, 21, 25, 20, 25, 14, 21, 25, 50, 39, 46, 20, 35, 45, 37, 46

1. Are there any outliers in this data set?
2. What calculator test (1-PropZInt, Z-Interval, or T-Interval), Excel, or StatCrunch function will you use to find the confidence interval?
3. Why do you use this test (and not one of the other 2 tests)?
4. Using a 95% confidence level, what is the confidence interval?
5. What is the point estimate for the population mean?
6. What is the margin of error?
7. Suppose you knew the standard deviation for all Americans' screen time was 4 hours. If you wanted your results to be within a margin of error of 0.25 hours, how many people would you have to survey (use a 95% confidence level)?
8. Name at least 2 ways this data could be biased and hence the confidence interval would not be a good estimate of the population mean.

Your final write-up should number (1-8) your answers to each question as well as an explanation of how you arrived at the answers. For example, please include what calculator functions or computations you are using to arrive at the confidence interval.

I realize similar questions were already asked. These aren't the same questions or the same data set. please also explain how to do this in excel.

For the Hawkins Company, the monthly percentages of all shipments received on time over the past 12 months are 78, 82, 84, 83, 83, 84, 88, 84, 82, 83, 84, and 83.

1.) Create a three-month moving average forecast against an exponential smoothing forecast with α=.2.

2.) Which forecasting method has the smallest error, use the Mean Square Error (MSE) metric as the measure of model accuracy?

3.) What is the forecast for the 13th month using a three month moving average?

Refer to the accompanying data set and construct a 90​% confidence interval estimate of the mean pulse rate of adult​ females; then do the same for adult males. Compare the results.

1. A random experiment consists of throwing a triangular shape with three faces three times. The first face has the number 1, the second face has the number 2 and the third face has the letter A.

1. List the sample space of the random experiment.   
2. Assume the faces are equally likely, what is the probability an outcome of experiment has at least one A?                                                                                                  
3. the letter A is three times likely to occur in a throw than the faces that has the numbers and the faces that has the numbers are equally likely. What is the probability an outcome of the experiment has at least one A?  

A fitness company is building a 20-story high-rise. Architects building the high-rise know that women working for the company have weights that are normally distributed with a mean of 143 lb and a standard deviation of 29 lb, and men working for the company have weights that are normally distributed with a mean of 165 lb and a standard deviation or 32 lb. You need to design an elevator that will safely carry 15 people. Assuming a worst case scenario of 15 male passengers, find the maximum total allowable weight if we want to a 0.98 probability that this maximum will not be exceeded when 15 males are randomly selected.

maximum weight =

Find the mean and standard deviation of the times and icicle lengths for the data on run 8903 in data data234.dat. Find the correlation between the two variables. Use these five numbers to find the equation of the regression line for predicting length from time. Use the same five numbers to find the equation of the regression line for predicting the time an icicle has been growing from its length. (Round your answers to three decimal places.)

time    length
10           2.5
20           1.9
30           3.8
40           5.4
50           6.4
60          10.1
70          9.5
80          12.1
90          14.1
100         13.9
110         18.9
120         19.1
130         21.5
140         23.3
150         26.5
160         28.2
170         29.6
180         28.8

In a study designed to test the effectiveness of magnets for treating back​ pain, 40 patients were given a treatment with magnets and also a sham treatment without magnets. Pain was measured using a scale from 0​ (no pain) to 100​ (extreme pain). After given the magnet​ treatments, the 40 patients had pain scores with a mean of 10.0 and a standard deviation of 2.8. After being given the sham​ treatments, the 40 patients had pain scores with a mean of 9.8 and a standard deviation of 2.32. Complete parts​ (a) through​ (c) below.

a. Construct the 99​% confidence interval estimate of the mean pain score for patients given the magnet treatment.

What is the confidence interval estimate of the population mean μ​?

__<μ​<__

b. Construct the 99% confidence interval estimate of the mean pain score for patients given the sham treatment.

What is the confidence interval estimate of the population mean μ​?

__<μ​<__

Air pollution control specialists in southern California monitor the amount of ozone, carbon dioxide, and nitrogen dioxide in the air on an hourly basis. The hourly time series data exhibit seasonality, with the levels of pollutants showing similar patterns over the hours in the day. On July 15,16 and 17, the observed level of nitrogen dioxide in a city�s downtown area for the 12 hours from 6:00 A.M. to 6:00 P.M. were as follows. 15-July 25, 28, 35, 50, 60, 60, 40, 35, 30, 25, 25, 20 16-July 28, 30, 35, 48, 60, 65, 50, 40, 35, 25, 20, 20 17-July 35, 42, 45, 70, 72, 75, 60, 45, 40, 25, 25, 25 a. Construct a time series plot. What type of pattern exists in the data? b. Use a multiple linear regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data: Hour 1 = 1 if the reading was made between 6 am and 7 am; 0 otherwise Hour 2 = 1 if the reading was made between 7 am and 8 am; 0 otherwise Hour 3 = 1 if the reading was made between 8 am and 9 am; 0 otherwise Hour 4 = 1 if the reading was made between 9 am and 10 am; 0 otherwise continue this pattern until Hour 11 = 1 if the reading was made between 4 pm and 5 pm' 0 otherwise Note that when the values of the 11 dummy variables are equal to 0, the observation corresponds to the 5 pm to 6 pm hour. c. using the equation developed in part (b), compute estimates of the levels of nitrogen dioxide for July 18 d. Let t = 1 to refer to the observation in hour 1 on July 15; t = 2 to refer to the observation in hour 2 of July 15 ..., and t = 36 to refer to the observation in hour 12 of July 17. using dummy variables devined in part (b) and t, develop an equation to account for seasonal effects and any linear trend in the time series. Based upon the seasonal effects in the data and linear trend, compute estimates of the levels of nitrogen dioxide for July 18 I only need the answer for part D. This is my 3rd time submitting for the same answer. Thanks.

At a charity event, a player rolls a pair of dice. If the player roles a pair (same number on each die), the player wins $10. If the two are exactly one number a part (like a five and a six), the player wins $6. IF the player roles a one and a six, they win $15. Otherwise, they lose. If it cost $5 to play, find the expected value. Write a complete sentence to explain what your answer means without words "Expected value". Show all work for full credit including the probability distribution.

1. Identify the explanatory and response variables in your study.

2. Explain why the study is an observational study or an experiment.

3. Can we conclude that there is a causal relationship between the explanatory and response variables?

This is the Study: https://www.sciencedaily.com/releases/2018/10/181009210738.htm

Planned intermittent fasting may help to reverse type 2 diabetes, suggest doctors writing in the journal BMJ Case Reports after three patients in their care, who did this, were able to cut out the need for insulin treatment altogether.

Around one in 10 people in the US and Canada have type 2 diabetes, which is associated with other serious illness and early death. It is thought to cost the US economy alone US$245 billion a year.

Lifestyle changes are key to managing the disease, but by themselves can't always control blood glucose levels, and while bariatric surgery (a gastric band) is effective, it is not without risk, say the authors. Drugs can manage the symptoms, and help to stave off complications, but can't stop the disease in its tracks, they add.

Three men, aged between 40 and 67, tried out planned intermittent fasting to see if it might ease their symptoms. They were taking various drugs to control their disease as well as daily units of insulin. In addition to type 2 diabetes, they all had high blood pressure and high cholesterol.

Two of the men fasted on alternate days for a full 24 hours, while the third fasted for three days a week. On fast days they were allowed to drink very low calorie drinks, such as tea/coffee, water or broth, and to eat one very low calorie meal in the evening.

Before embarking on their fasting regime, they all attended a 6-hour long nutritional training seminar, which included information on how diabetes develops and its impact on the body; insulin resistance; healthy eating; and how to manage diabetes through diet, including therapeutic fasting.

They stuck to this pattern for around 10 months after which fasting blood glucose, average blood glucose (HbA1c), weight, and waist circumference were re-measured.

All three men were able to stop injecting themselves with insulin within a month of starting their fasting schedule. In one case this took only five days.

Two of the men were able to stop taking all their other diabetic drugs, while the third discontinued three out of the four drugs he was taking. They all lost weight (by 10-18%) as well as reducing their fasting and average blood glucose readings, which may help lower the risk of future complications, say the authors.

Feedback was positive, with all three men managing to stick to their dietary schedule without too much difficulty.

This is an observational study, and refers to just three cases-all in men. As such, it isn't possible to draw firm conclusions about the wider success or otherwise of this approach for treating type 2 diabetes.

"The use of a therapeutic fasting regimen for treatment of [type 2 diabetes] is virtually unheard of," write the authors. "This present case series showed that 24-hour fasting regimens can significantly reverse or eliminate the need for diabetic medication," they conclude.

Suppose

239239

subjects are treated with a drug that is used to treat pain and

5151

of them developed nausea. Use a

0.100.10

significance level to test the claim that more than

2020​%

of users develop nausea.

Identify the null and alternative hypotheses for this test. Choose the correct answer below.

A.

Upper H 0H0​:

pequals=0.200.20

Upper H 1H1​:

pless than<0.200.20

B.

Upper H 0H0​:

pequals=0.200.20

Upper H 1H1​:

pgreater than>0.200.20

C.

Upper H 0H0​:

pequals=0.200.20

Upper H 1H1​:

pnot equals≠0.200.20

D.

Upper H 0H0​:

pgreater than>0.200.20

Upper H 1H1​:

pequals=0.200.20

Identify the test statistic for this hypothesis test.

The test statistic for this hypothesis test is

nothing.

​(Round to two decimal places as​ needed.)

Identify the​ P-value for this hypothesis test.

The​ P-value for this hypothesis test is

nothing.

​(Round to three decimal places as​ needed.)

Find the optimal values of x and y using the graphical solution method: Max x + 5y subject to: x + y ≤ 5 2x + y ≤ 8 x + 2y ≤ 8 x ≥ 0, y ≥ 0

A sample of n = 16 individuals is selected from a population with µ = 30. After a treatment is administered to the individuals, the sample mean is found to be M = 33. a. If the sample variance is s2 = 16, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. b. If the sample variance is s2 = 64, then calculate the estimated standard error and determine whether the sample is sufficient to conclude that the treatment has a significant effect? Use a two-tailed test with α = .05. c. Describe how increasing variance affects the standard error and the likelihood of rejecting the null hypothesis