Measurement - Statistics Assignment Help

Assignment Task

1. Consider the boxplot below:

a) What proportion of measurements fall between 40 and 85?

b) Use the 1.5 IQR rule to determine whether the measurement at 5 is an outlier.

c) Would the mean be greater than or less than the median for this data set? Explain your choice.

2. Let z be the standard normal variable. Find the proportion of all z's that are:

a) Greater than ?2.13

b) Between ?2.13 and 1.39

3. What value of z is greater than 68% of all other z values?

4. Adult male heights have mean 175 cm and standard deviation 12 cm. Use the 68-95-99.7% rule to determine the proportion of adult males with height between 139 cm and 187 cm.

5. The table below lists the weights of girls in a grade 7 gym class.

Create an Ogive for the data set

6. Tounces has two children, Jake and Cooper. Both children are stars in their favourite sports. Jake is able to run the 100 meter sprint in 24 seconds in a group of children where the mean is 27 seconds and the standard deviation is 1.5 seconds. Cooper can throw a shot put 20 feet in a group of children where the mean is 15 feet and the standard deviation is 2 feet. Which child is more exceptional compared to the others in their group? Explain your reasoning.

7. A study shows that the number of hour spent weekly on Facebook by college students has mean of 30 hours and standard deviation 4 hours. The study later claims that at least 20% of college students spend more than 40 hours weekly on Facebook. Explain why this later (the 20%) claim is impossible (Hint: Use Chebyshev’s Theorem)

8. Describe the level of measurement (nominal, ordinal, interval, ratio) for the data set

a) Students rate the difficulty of a test as easy, fair or difficult.

b) Children describe their favorite colours.

9. Give your own example of a discrete data set.

10. During the Vancouver Sun Run, finishing times were normally distributed with a mean of 68 minutes and a standard deviation of 12 minutes.

a) What proportion of runners finished the run in less than 47 minutes?

b) What proportion of runners required between 47 minutes and 95 minutes?

c) The fastest 3% of runners were given a cash prize. How quickly did a runner need to complete the run in order to obtain a cash prize?

11. In the scatterplot below, the outlier was discovered to be an error.

12. In a study on smoking and life expectancy conducted in various cities throughout the world, it was found that the correlation between x = percentage of the adult population that smokes and y = life expectancy is r = -0.7. What percentage in the variation of life expectancy is unexplained by the percentage of the adult population that smokes in the linear model.

13. A travel writer recorded the distance x (one way) and cost y for various Westjet flights

a) What is the explanatory variable? What is the response variable?

b) Create a scatterplot for the data. Use the scatterplot to describe the linear association that exists.

c) What is the value of the correlation coefficient r? (You may use your calculator)

d) Find the equation of the least squares regression line and plot this line on your scatterplot above. (You may use your calculator)

e) Find the residual when predicting the cost for a 700 km flight?

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