1)A new chemical has been found to be present in the human bloodstream, and a medical group would like to study the presence of this chemical in some samples of patients. The presence of the chemical in a patient is measured by a score representing the 'parts per billion' in which that chemical appears in the blood. It is known that, on this scale, men have an average score of 810.9 and a standard deviation of 58. It is also known that women have an average score of 835.48 and a standard deviation of 21.

An assistant in the medical team has been handed a sample of 100 scores. The assistant knows that all of the scores are from one of the two genders, but the sample was not documented very well and so they do not which gender this is. Within the sample, the mean score is 825.4.

a)Complete the following statements. Give your answers to 1 decimal place.

If the sample came from a group of 100 men, then the sample mean is ______ standard deviations above the mean of the sampling distribution. In contrast, if the sample came from a group of 100 women, then the sample mean is _______ standard deviations below the mean of the sampling distribution.

b)Based on this, the assistant is more confident that the sample came from a group of 100 _____men or women_____

2)The life span at the birth of humans has a mean of 87.74 years and a standard deviation of 17.76 years. Calculate the upper and lower bounds of an interval containing 95% of the sample mean life spans at birth based on samples of 105 people. Give your answers to 2 decimal places.

a)Upper bound = _________ years

b)Lower bound = ______ years

3)A drug made by a pharmaceutical company comes in tablet form. Each tablet is branded as containing 120 mg of the particular active chemical. However, variation in manufacturing results in the actual amount of the active chemical in each tablet following a normal distribution with mean 120 mg and standard deviation 1.665 mg.

a)Calculate the percentage of tablets that will contain less than 119 mg of the active chemical. Give your answer as a percentage to 2 decimal places.

Percentage = %

b)Suppose samples of 12 randomly selected tablets are taken and the amount of active chemical measured. Calculate the percentage of samples that will have a sample mean of less than 119 mg of the active chemical. Give your answer as a percentage to 2 decimal places.

Percentage = %

4)

During its manufacturing process, Fantra fills its 20 fl oz bottles using an automated filling machine. This machine is not perfect and will not always fill each bottle with exactly 20 fl oz of soft drink. The amount of soft drink poured into each bottle follows a normal distribution with mean 20 fl oz and a standard deviation of 0.17 fl oz.

The Fantra quality testing department has just carried out a routine check on the average amount of soft drink poured into each bottle. A sample of 25 bottles was randomly selected and the amount of soft drink in each bottle was measured. The mean amount of soft drink in each bottle was calculated to be 19.90 fl oz. The Fantra Chief Executive Officer believes that such a low mean is not possible and a mistake must have been made.

Calculate the probability of obtaining a sample mean below 19.90 fl oz. Give your answer as a decimal to 4 decimal places.

probability =

The type of household for the U.S. population and for a random sample of 411 households from a community in Montana are shown below.

Use a 5% level of significance to test the claim that the distribution of U.S. households fits the Dove Creek distribution.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: The distributions are different.
H₁: The distributions are the same.

H₀: The distributions are different.
H₁: The distributions are different.    

H₀: The distributions are the same.
H₁: The distributions are different.

H₀: The distributions are the same.
H₁: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to two decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes

No    

What sampling distribution will you use?

uniform

chi-square    

binomial Student's t

normal

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)


(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.    

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is sufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

At the 5% level of significance, the evidence is insufficient to conclude that the community household distribution does not fit the general U.S. household distribution.

Political polling relies heavily on sampling techniques, which allow us to make inferences about an entire population based on only a portion of the population. However, the "Brexit" referendum in the United Kingdom and several elections in the United States since 2016 have called into question the accuracy of much political polling

1. What explains the inaccuracy of many pre-election polling data since 2016? Provide specific case examples.

2. What statistical techniques could be used to improve the accuracy of polling?

3. Has the value of political polling diminished? What is your personal perception of political polling?

In each of the following sets of variables, which are likely candidates to be treated as independent and which as dependent within a research study?

• Gender, alcohol consumption, and driving record In the following set of variables

• High school GPA (grade point average), university freshman year GPA, choice of university major (selected before enrollment), race/ethnicity, and gender

• Age, race/ethnicity, smoking habits, and occurrence of breast cancer

Explain each answer please.

The administration of a local college states that the average age of its students is 28 years. Records of a random sample of 100 students give a mean age of 31 years. Using a population standard deviation of 10 years, test at the 5% significance level whether there is evidence that the administration’s statement is incorrect.

State clearly your null and alternative hypotheses.

Imagine you take the SAT which has a µ = 500 and σ = 100 and receive a score of X = 600. What proportion of people did better than you?

(round to two decimals)

EXPLAIN HOW YOU GOT THE ANSWER

A student asked 7 random people that graduated last year their GPA and starting salary. The following table includes the responses:

1. What is the coefficient of correlation?

a) -0.9857

b) -0.5854

c) 0.5854

d) 0.9857

2.  What is the slope of the regression equation?

a) 5.85

b) 7.81

c) 16.78

d) 67.85

3.  What is the regression equation?

a) GPA=7.81 + 14.57*$Starting Salary

b) GPA = 16.58+0.648*$Starting Salary

c) $Starting Salary=0.6048 + 16.58*GPA

d) $Starting Salary = 14.57 +7.81*GPA

3. Based on the data above what does the R² correlation coefficient indicate?

a) There is a positive linear relationship between GPA and starting salary.

b) This is not a good model for this data.

c) This is a fairly strong model for this data.

d) Both a and c.

________a number that is used to represent a population characteristic and that generally cannot be determined easily

________a method for selecting a sample and dividing the population into groups; use simple random sampling to select a set of groups. Every individual in the chosen groups is included in the sample.

________a method for selecting a sample used to ensure that subgroups of the population are represented adequately; divide the population into groups. Use simple random sampling to identify the number of individuals from each group.

_____ the set of all possible outcomes of an experiment

________a numerical characteristic of the sample

________all individuals, objects, or measurements whose properties are being studied

• _______ deals with estimating a population parameter based on a sample statistic.
• _______ the decision is to reject the null hypothesis when, in fact, the null hypothesis is true.
• _______ probability of a Type I error.
• _______ is a statement about the value of a population parameter
• _________ states that if the size n of the sample is sufficiently large, then the distribution of the sample means and the distribution of the sample sums will approximate a normal distribution regardless of the shape of the population.
• _______ the probability that an event will happen purely by chance assuming the null hypothesis is true.
• _______ the decision is not to reject the null hypothesis when, in fact, the null hypothesis is false.
• _______ is a single number computed from a sample and used to estimate a population parameter.
• ____________ is an interval estimate for an unknown population parameter.

Cluster Sampling

Sample Space

Population

Stratified Sampling

Parameter

Statistic

1. p-value
2. Confidence Interval
3. Inferential Statistics
4. Level of Significance
5. Type II Error
6. Hypothesis
7. Central Limit Theroem
8. Type I Error
9. point estimate

At one point the average price of regular unleaded gasoline was

​$3.543.54

per gallon. Assume that the standard deviation price per gallon is

​$0.080.08

per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within

33

standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within

2.52.5

standard deviations of the​ mean? What are the gasoline prices that are within

2.52.5

standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between

​$3.383.38

and

​$3.703.70​?

The methods of parametric statistics (like t-tests, z-intervals, etc.) can be applied to nominal or ordinal data. Question 1 options: True or False

Question 2 When only ordinal-level data are available, Spearman’s rank correlation can be used to analyze the association between two variables. Question 2 options: True or False

Number of Police Officers (X)    Number of Crimes (Y)

0    10

20    10

   30    40


a. Calculate the correlation coefficient and the covariance

b. Calculate the regression coefficient of the slope.

c. State the regression equation.

d. Interpret the meaning of the intercept and slopes in this equation. Be sure to explain using units.

e. Predict the number of crimes when the number of police officers is 7.

A mill operator is concerned that bags are not being filled to the stated 1000g of grain. 20 bags are randomly weighed and results recorded. There is a sign on the machine that states "grain volumes dispensed follow a normal distribution". a) If a one sample t-test is used, write down the decision rule in terms of a test statistic and calculate the value of the test statistic manually. Use 5% level of significance. b) State the two assumptions of this test and their likely validity.

Bag Weight
1,968.22
2,918.98
3,942.76
4,1024.02
5,988.96
6,1057.26
7,987.28
8,970.06
9,947.76
10,1003.18
11,1005.7
12,1076.16
13,931.36
14,990.06
15,950.64
16,1058.82
17,1036.26
18,928.64
19,898.16
20,978.54

Describe four methods of sampling, and provide examples of each. How could each of these methods be useful in some area of business? Do you think any more method would be more valuable than others? Why or why not?

Directions: Use the Bivatiate Correlation function and the Options submenu to answer each of the questions based on the above scenario.

The superintendent has continued the examination of data by examining the relationship between attendance rate and percent of students eligible for free or reduced priced lunch. The district data used for the analysis are contained below.

1. What is the mean percent of students receiving free or reduced lunch? What is the mean attendance rate?

51.97 free or reduced

94.16 attendance

2. What are the standard deviations for the percent of students receiving free or reduced lunch and attendance rate?

15.68 free or reduced

1.71 attendance

3. State an appropriate null hypothesis for this analysis.

4. What is the value of the correlation coefficient?

5. Based on the value of the correlation coefficient, how would you classify the strength of this relationship?

6. Based on the information from the scenario, what is the appropriate value for the degrees of freedom?

7. What is the reported level of significance?

8. Present the results as they might appear in an article. This must include a table and narrative statement that reports and interprets the results of your analysis.

Note: The table must be created using your word processing program. Tables that are copied and pasted from SPSS are not acceptable.

Problem 1

A farm has been experimenting with a special diet for its horses. The feed components for the diet are

a standard feed product, a vitamin-enriched oat product, and a new vitamin and mineral feed additive

(detail below). The minimum daily diet requirements for each horse are 3 units of ingredient A, 6 units

of ingredient B, and 4 units of ingredient C. In addition, to control the weight of the horses, the total

daily feed for a horse should not exceed 6 pounds. The farm would like to determine the minimum-

cost mix that will satisfy the daily diet requirements.

Ingredients [in units] to Produce One Pound of Special Die

On a separate piece of paper, define the variables and formulate the mathematical model for this problem.

Enter the model into Excel's Solver and solve it. How many pounds of Standard product, Enriched Oat, and Additive should be used in the mix to generate the lowest possible total cost?

Please complete on excel using solver so I can see how to format and what cells to link