## Question

1. Use appropriate R codes to access data from the Getting To Know You Survey.

NoU = read.csv(“Getting2NoUFall2018.csv”)

2. Construct a histogram and a Q-Qplot for variables “height” and “Shoe size”. Include both plots in your submission. Describe the shape of the distribution.

3. Find the sample size, sample mean, Sample standard deviation and standard error. of "family Income" using the length(), mean(), sd() commands. Describe what standard error measures. Cut and paste your R output into your submission.

4. Now use t.test() to compute the 95% confidence interval of "family income". Does the R output match your results in part (c)? Copy and paste your R output. You need to interpret the results.

5. Conduct t.test of means between "high.school.GPA" and "college.GPA".You need to write R codes and paste your outputs and then interpret your results.

6. Conduct t.test of means to compare "Hair cost" between males and females.You need to write R codes and paste your outputs and then interpret your results.

7. What is the Probability that any student choosing at random is a male?

8. What is the Probability that any student choosing at random is a female?

9. Compute the respective probabilities of being a Junior, Sophomore, Senior and Freshman.

10. What is the Conditional probability that a male student chosen at random is a Freshman?

11. If it is assumed that family income is normally distributed, what is the Probability of choosing a student with annual family income less than $50,000?

12. What is the proportion of International students?

13. How many international students have annual family income greater than $50,000?

14. What is the proportion of students who reside on Campus?

15. Determine the respective probabilities of being Liberal, Moderate and conservatives.

16. What is the Probability of being an International student?

17. Obtain Basic statistical summary using R codes for Height, Age, Shoe size and Ideal weights.

18. How many students took part in the survey?

19. How many were from Asia?

20. What is the probability that any chosen student is from North America?

## Solution Preview

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# 2par(mfrow=c(2,2))

hist(NoU$height, freq=FALSE, breaks=20)

hist(NoU$shoe.size, freq=FALSE, breaks=50)

qqnorm(NoU$height)

qqline(NoU$height)

qqnorm(NoU$shoe.size)

qqline(NoU$shoe.size)

# The height does not appear to follow the normal distribution

# at right tail from the qqplot and the histogram

# show it is slightly skewed to the right.

# It may fit better to the chi-squared distribution.

# The shoe.size data fits very well to the normal

# distribution with very small spread except for one

# outlier that is very huge.

# 3.

length(NoU$family.income)

# [1] 491

# mean(NoU$family.income, na.rm=TRUE)

# sd(NoU$family.income)

# mean and standard deviation cannot be calculated because they are factor

# describing the interval of income level....