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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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