Statistics assignment using R program
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1. The technical operations department of an Internet Service Provider (ISP) wants to ensure that the mean target upload speed for all Internet service subscribers is at least 0.97 on a standard scale in which the target value is 1.0. The data set “AMS9.csv” represents the upload speed measured 50 times in a day.
a. What type of test should we use?
b. At the 0.10 level of significance, can you test whether the mean upload speed is less than 0.97? Please plot the following graph as shown. What is the absolute value of the critical point?

c. Can you confirm your conclusion in part a using p value approach? Can you also replicate p value from t.test using the pt function?

d. Can you confirm your conclusion in part a using CI approach? No need to use CI function from Question 1. You can use result generated from t.test directly.

2. Bioboom today identified the top Biomed startup firms in 10 geographic regions across the United States. A characteristic description of the Biomed startup firms in the Southeast and Gulf Coast regions included the number of partners in the firm (“BRPartners2.csv”). We can assume the variance between two populations are equal. We want to test whether the mean numbers of partners between the two regions are different.
a. What type of test should we use?
b. At the 0.05 level of significance, can you graph the critical value approach?
c. Can you carry out the same test using p value approach and duplicate the p value from t.test?
d. Can you carry out the same test using CI approach?

3. The variable of interest is defined as the reported pain relieving time, in minutes, from the time the medication is taken to the time a patient reports positive response. Data are in “ReTime.csv”. We can assume the variance between two populations are equal. We want to determine the response time of A is shorter than B.
a. What type of test should we use?
b. At the 0.10 level of significance, can you graph the critical value approach?
c. Can you carry out the same test using p value approach and duplicate the p value from t.test?
d. Can you carry out the same test using CI approach?

4. Multiple myeloma, or blood plasma cancer, is characterized by increased blood vessel formulation (angiogenesis) in the bone marrow that is a predictive factor in survival. One treatment approach used for multiple myeloma is stem cell transplantation with the patient’s own stem cells. The data stored in “Myeloma.csv” represent the bone marrow microvessel density for patients who had a complete response to the stem cell transplant (as measured by blood and urine tests). The measurements were taken immediately prior to the stem cell transplant and at the time the complete response was determined. We want to determine whether the mean bone marrow microvessel density is higher before the stem cell transplant than after the stem cell transplant.
a. What type of test should we use?
b. At the 0.01 level of significance, can you graph the critical value approach?
c. Can you carry out the same test using p value approach and duplicate the p value from t.test?
d. Can you carry out the same test using CI approach?

 

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Statistics
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Overview I have provided you with an excel file (Exam1_data.xlsx) that contains 5 pyrethroid pesticide metabolites measured in dust samples collected in 85 homes and day-care facilities. The file contains two spreadsheets. The first sheet (Metabolite_data) contains the sample data, having concentrations of the metabolites reported in ng/g. Concentrations below the method detection limit are indicated by ‘nd’. The second sheet (MDL_data) contains the method detection limits for each of the metabolites, also reported in units of ng/g. These data are from a research publication that has also been provided to you for added perspective. It is not a requirement to read the paper in detail to perform the tasks associated with this Exam. Exam Instructions 1) Read these instructions completely and review the data set. Based on what you have learned thus far perform the following steps. 2) Detection Frequency and Data Substitution a. Calculate the frequency of detection for each of the analytes. Present the results in tabular form. [5 pts] b. Make a decision regarding the substitution of values that were below the detection limit. This could be one of the analytes or all of them, but your decision will not be none of them. Describe your reasoning for selecting which analytes to substitute the below detection data. [10 pts] c. Substitute the ‘nd’ values using a method of your choosing. Describe your reasoning for selecting the method to substitute the below detection data. [10 pts] d. Calculate the concentration distributions for each metabolite as is, and for where an analyte has substituted values). Present results in a tabular form, using the following percentiles of the distribution (0, 1, 5, 10, 25, 50, 75, 90, 95, 99, 100) and also presenting the arithmetic mean and standard deviation. Describe any differences in the distribution statistics (if any). [30 pts] e. Visually compare and present the two distributions (with and without data substituted) for analytes where you have substituted for the below-detection data using an E-CDF. Describe any differences in the distribution (if any). [15 pts] 3) Evaluation for Outliers a. Approximate the distribution forms using QQ plots to determine normality. [10 pts] b. Based on the distribution form, select an appropriate approach (either a parametric or non-parametric test) to conduct an outlier analysis. Discuss approach selected and the reasoning for its selection. [10 pts] c. Where potential outliers have been identified (if any), calculate new distribution statistics (i.e., means, standard deviations, percentiles) for the new metabolite distribution. Discuss differences to the distributions (with all data and following outlier removal, if any) by comparing their descriptive statistics [10 pts] 4) Provide tables and figures in excel sheets

 

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Statistics
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Q1) Independent-Samples t Test (25 points total)
A psychologist would like to evaluate the effectiveness of alunchtime walking programon job satisfaction. The psychologist conducted a small study to examine the potential effect of the 6-weeklunchtime walking program on job satisfaction as measured on a 10-item scale at the end of the program.A composite score ranging from 0 to 10 was computed from the scale for each subject with 10 indicating the highest level of job satisfaction. The psychologist recruited 10employees to participate in lunchtime walking program and 12employees with similar demographics who do not participate in the lunchtime walking program. The data are listed in the table below. The psychologist strongly suspects based on prior research that job satisfaction scores will rise as a result of the walking program.The alpha level is set at .05 for the hypothesis test.

Lunchtime walking program No lunchtime walking program
Subject ID # Job satisfaction score Subject ID # Job satisfaction score
1 7 11 5
2 5 12 8
3 8 13 6
4 6 14 5
5 5 15 7
6 9 16 8
7 8 17 6
8 8 18 7
9 6 19 9
10 6 20 6
21 7
22 5

What is the dependent (outcome) variable? What is the independent (grouping) variable? (1 point total: .5 for each variable)

Create the null and alternative hypotheses for this study, using both words and symbol notation.(2 points total: 1 per hypothesis- .5 for written format, .5 for notation)

Calculate M1 andM2.(2 points total: 1 point per sample mean- .5 for work, .5 for answer)

Calculate df1 , df2, and dftotal.(2 points total: 1 for df1 and df2, 1 for total df, including work)

Calculate s21 and s22. (estimated variance for population 1 and variance for population 2) (4 points total: 2 points for each variance. 1 for work and 1 for result)

Calculate the pooled variance for the two populations.(2 points total: 1 point for work, 1 point for result)

Use the pooled variance to calculate the variance for sampling distribution 1 and the variance for sampling distribution 2.(2 points total: 1 for work and 1 for result)

Hint: Sampling distribution derives from the original population and it consists of means of all possible samples drawn from the original population.

Calculate standard deviation of the comparison distribution.(2 points total: 1 for work and 1 for result)

Hint: This is the distribution consisting of differences between means and its standard deviation is the denominator of the t statistic formula.

Calculate the t statistic.(2 points total: 1 for work and 1 for result)

Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)

Determine the critical t value(s) for this hypothesis test based on the degree of freedom, from (d), and the preset alpha level. (1 point total)

Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then make a decision about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis.(1 point total: .5 for comparison, .5 for decision)

Calculate the pooled standard deviation for the populations and then use it to calculate the standardized effect size of this test. (2 point total: 1 for pooled standard deviation, 1 for effect size. Deduct .5 if a result is wrong but the process is correct.)

Q2) Independent-Samples t-Test (25 points total)
A psychologist is interested in understanding the effect of nightly meditation on hours of sleep. The subjects in one group participated in meditation for 20 minutes a night for six weeks. Subjects in the other group did not engage in any nightly meditation.Participants’ sleep was measured with the use of a sleep tracker worn on the wrist. The researcherwould like to run a hypothesis test with α = .05to see if there is a significant difference in sleep hours betweenthose who engaged in nightly meditation and those who did not. The psychologist does not predict whether those who meditate will sleep more or less hours on average, but rather is interested in any direction of the difference.

Meditation program No meditation program,
Participant Average sleep hours Participant Average sleep hours
1 4 11 5
2 7 12 7
3 6 13 8
4 9 14 7
5 7 15 6
6 6 16 6
7 8 17 4
8 9 18 9
9 7 19 7
10 6 20 6

What is the dependent (outcome) variable? What is the independent (grouping) variable? (1 points total: .5 per variable)

Create the null and alternative hypotheses for this study, using both words and symbol notation.(2 points total: 1 per hypothesis- .5 for written format, .5 for notation)

Calculate M1 andM2.(2 points total: 1 point per sample mean- .5 for work, .5 for answer)

Calculate df1 , df2, and dftotal.(2 points total: 1 for df1 and df2 which are the same, 1 for total df, including work)

Calculate s21 and s22. (estimated variance for population 1 and variance for population 2) (4 points total: 2 points for each variance. 1 for work and 1 for result)

Calculate the pooled variance for the two populations.(2 points total: 1 point for work, 1 point for result)

Use the pooled variance to calculate the variance for sampling distribution 1 and the variance for sampling distribution 2.(2 points total: 1 for work and 1 for result)

Hint: Sampling distribution derives from the original population and it consists of means of all possible samples drawn from the original population.

Calculate standard deviation of the comparison distribution.(2 points total: 1 for work and 1 for result)
Hint: This is the distribution consisting of differences between means and its standard deviation is the denominator of the t statistic formula.

Calculate the t statistic.(2 points total: 1 for work and 1 for result)

Considering the research question and the hypotheses, should the test be one-tailed or two-tailed? Why? (2 points total: 1 for each answer)

Determine the critical t value(s) for this hypothesis test based on the degree of freedom, from (d), and the preset alpha level. (1 point total)

Compare the calculated t statistic with the critical t value by stating which is more “extreme”, and then make a decision about the hypothesis test by stating clearly “reject” or “fail to reject” the null hypothesis.(1 point total: .5 for comparison, .5 for decision)

Calculate the pooled standard deviation for the populations and then use it to calculate the standardized effect size of this test. (2 point total: 1 for pooled standard deviation, 1 for effect size. Deduct .5 if a result is wrong but the process is correct.)

 

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Descriptive Statistics
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A major client of your company is interested in the salary distributions of jobs in the state of Minnesota that range from $30,000 to $200,000 per year. As a Business Analyst, your boss asks you to research and analyze the salary distributions. You are given a spreadsheet that contains the following information:
• A listing of the jobs by title
• The salary (in dollars) for each job
The client needs the preliminary findings by the end of the day, and your boss asks you to first compute some basic statistics.
Background information on the Data
The data set in the spreadsheet consists of 364 records that you will be analyzing from the Bureau of Labor Statistics. The data set contains a listing of several jobs titles with yearly salaries ranging from approximately $30,000 to $200,000 for the state of Minnesota.

 

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