USING R, R studio and by hand, calculate the following 15 drops of a paper helic

Question

USING R, R studio and by hand, calculate the following

15 drops of a paper helicopter, times are recorded

Median : 1.8

mode: 1.9

variance: .0169

1a. Using R, plot the distribution of the drop times using the hist(dataframe name$drop times). Show your work and check it using R, provide a screenshot of the code and output. Do you see strong evidence that the drop time data is not normally distributed? Why or why not? (Just eyeball it – look at the shape of the distribution as compared to what a normal distribution looks like.)

b. Plot the distribution of the drop time data again. Show your work, and check it against R. Provide a screenshot of the code and output. Do you see strong evidence that the data does not have a 2 distribution? Why or why not? (Just eyeball it – look at the shape of the distribution as compared to what a 2 distribution looks like.)

c. Assume that the 15 drops are a sample from a normal population, regardless of your answer to 1a. We’re going to use that sample to estimate the average drop time of a population of many drops, along with the variance of drop times.

i. Identify your point estimate of the population mean. (Hint: you’ve already calculated it!)

ii. Identify your point estimate of the population variance.

iii. Compute the standard error of your point estimate of population mean.

2. A normal population has mean 100 and variance 25. How large must the random sample be if you want the the standard error of the sample be 1.5

3. The amount of time a passenger waits at an airport check-in counter is random variable with mean 8.2 minutes and standard deviation of 1.5 minutes. Suppose a random sample of 49 customers is observed. Calculate the probability that the average waiting time waiting in line for this sample is (a) less than 10 minutes (b) between 5 and 10 minutes

4. A computer software package calculated some summaries of sample data. The results are below. Please fill in the blanks and estimate the mean of the population from which the sample was drawn.

5. Suppose that two independent random samples of size n1 and n2 from two normal distributions are available. Explain how you would estimate the standard error of the difference in sample mean with the bootstrap method (you can write a pseudo code).

Explanation / Answer

(2)

Mean, m = 100

Standard deviation, S = 250.5 = 5

Assume that the sample size is 'n'

Standard error, SE = S/n0.5

Putting values:

1.5 = 5/n0.5

Solving we get:

n = 11.12

So, the sample size must be atleast 12.

(3)

Mean, m = 8.2

Standard deviation, S = 1.5

Sample size, n = 49

Since you have not specified the nature of the distribution, I am assuming normal distribution

Calculating Standard error:

SE = S/n0.5 = 1.5/490.5 = 0.214

(a)

At X = 10, the z-score is:

z = (X-m)/SE = (10-8.2)/0.214 = 8.411

The corresponding p-value for this z-score is:

p = 1

(b)

At X = 5, the z-score is:

z = (X-m)/SE = (5-8.2)/0.214 = -14.95

The corresponding p-value for this z-score is:

p = 0

So, the reqd probability is: 1-0 = 1

Hope this helps !

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