Assignments on Hypothesis Test

1.     Import the given dataset Data_File_Sup.xlsx. State whether BMI is normally distributed according to the Age by using a proper graph and statistical method. Explain your answer.

 

2.     Import the given dataset Data_File_Sup.xlsx. Test the hypothesis on the sample that “Income of people living in Rural areas is lower than that of Urban areas”. Use proper hypothesis testing method with a confidence level of 0.95.

 

3.     Import the given dataset Data_File_Sup.xlsx. Test the hypothesis on the sample that “BMI of Male population is not equal to that of Female population”. Use proper hypothesis testing method with a confidence level of 0.95.

 

4.     Import the given dataset Data_File_Sup.xlsx. Can the sample be regarded as drawn from normal population with mean Age of 47 and standard deviation of 3, at 5% significance? Use proper hypothesis testing method and explain your answer.

 

5.     Import the built-in ToothGrowth dataset in R. The dataset comprises the length of odontoblasts (cells responsible for tooth growth) in 60 guinea pigs. Each animal received one of three dose levels of vitamin C (0.5, 1, and 2 mg/day) by one of two delivery methods, orange juice (OJ) or ascorbic acid (VC). Test the hypothesis that the length of odontoblasts for OJ on average is 4 more than that for VC.

 

6.     Write a R program to compute the approximate Z for Single Sample Sign Test for large dataset.

 

7.     Test the claim that the median age of doctors in our state is at least 42 years. The age 32 doctors are given bellow (in years).

Use the sign test at the 5% level of significance to test the claim by critical value method.

 

8.     Import the dataset mice.csv. Here effect of a drug on blood sugar level is observed on 10 mice. Check whether the drug makes a significant difference in blood sugar level.

 

9.     Import the Titanic dataset in R. Test whether there is a significant difference in ages between male and female passengers in the dataset.

 

10.  a) Import the ‘mtcars’ dataset in R.

b) Show the details of each variable in the dataset.

c) Find the Average mileage of the cars with 6 cylinders.

d) Show the distribution of cars by number of cylinders using a barplot or histogram.

e) Analyze the relationship between Gross Horsepower and the number of Cylinders.

 

11.  a) Import the data from the following link: https://stats.idre.ucla.edu/stat/data/binary.csv

b) Present the summary of the data.

c) Now do Logistic Regression to find out relation between variables that are affecting the

admission of a student in a institute.

d) Based on his or her GRE score, find out GPA obtained and rank of the student.

 

12.  a) Assume that the test scores of a college entrance exam fits a normal distribution.

Furthermore, the mean test score is 72, and the standard deviation is 15.2. What is the percentage of students scoring 84 or more in the exam?

b) If there are twelve cars crossing a bridge per minute on average, find the probability of having seventeen or more cars crossing the bridge in a particular minute.

c) Suppose there are twelve multiple choice questions in an English class quiz. Each question has five possible answers, and only one of them is correct. Find the probability of having four or less correct answers if a student attempts to answer every question at random.

 

13.  A pharmaceutical company is testing a new drug designed to lower cholesterol levels. They recruit 12 patients and measure their LDL cholesterol levels before administering the drug and again after one month of treatment. The data below shows the LDL cholesterol levels (in mg/dL) for each patient: 179, 136, 162, 168, 172, 87, 153, 176, 127, 156, 167, 166.

Using the Wilcoxon Signed-Rank Test:

a) Is there a significant difference in LDL cholesterol levels before and after treatment?

b) Is there evidence to suggest that the new drug significantly reduces LDL cholesterol levels?