Exam 1 Stats

Which of the following are true statements about the correlation coefficient r?

(i)The correlation r is always between -1 and 1 .(ii)Correlation r measures how well a straight line models your data.(iii)Correlation r varies with your units of measurement. (iv)The square of the correlation is the coefficient of determination. (d) (i), (ii) and (iv).

The following two multiple-choice questions refer to cats. The weights of the cats in Questions 5 and 6 are normally distributed with a mean of 9.5 pounds and a standard deviation of 1.5 pounds. How much do the heaviest 2.5% of these cats weigh?

12.5 pounds or more

The following two multiple-choice questions refer to cats. The weights of the cats in Questions 5 and 6 are normally distributed with a mean of 9.5 pounds and a standard deviation of 1.5 pounds. What percentage of these cats weigh less than 8 pounds?

16%

Suppose we have recorded the weights and heights of 50 people. We decide to regress weight (Y) on height (X) because we wish to predict Y from X. We find that the coefficient of determination is 25%. Suppose we change our mind, and now want to regress height on weight. What will be the coefficient of determination for this new regression?

25%

We are interested in predicting how far a frog can jump (measured in cm), based on it's leg length (also in cm). We collect data on 50 frogs, allowing each frog one leap. We find the correlation, r is 0.7, the mean of the leg length is 16cm, with a standard deviation of 2cm, and the mean jumping distance is 20cm, with a standard deviation of 5cm. A frog with legs 20cm long would be predicted to jump

27cm

We are interested in predicting how far a frog can jump (measured in cm), based on it's leg length (also in cm). We collect data on 50 frogs, allowing each frog one leap. We find the correlation, r is 0.7, the mean of the leg length is 16cm, with a standard deviation of 2cm, and the mean jumping distance is 20cm, with a standard deviation of 5cm. What proportion of variation in jumping distances is due to the linear relation to leg length?

49%

The on-time rates for the airlines AS and AB for flights from Seattle are respectively;

76.7% and 60%

The on time rates for airlines AS and AB for all passengers are respectively;

78% and 79%

What percentage of Phoenix passengers use AB?

86%

A 2331 statistics student has a grade of 86% going into the final exam. The final exam is worth 20% of the overall grade. What percentage score does the student need on the final exam to ensure she gets at least 80% overall in the class?

86% of 80 points is 0.86x80=68.8. So to get to 80 points total the student would need 11.2 points more (80-68.8). Since the exam is worth 20 points, this is 11,2/20=56%,

What percentage of Seattle passengers use AS?

88%

The on-time rates for airlines AS and AB for flights from Phoenix are respectively;

89% and 83%

Suppose that two variables X and Y are known to have a correlation of 0.98. Which of the following statements do we know must always be true?

A regression of Y on X will produce a line with a positive slope

The mode is another name for the median.

False

The standard deviation is an outlier-resistant measure of variation.

False

We are interested in predicting how far a frog can jump (measured in cm), based on it's leg length (also in cm). We collect data on 50 frogs, allowing each frog one leap. We find the correlation, r is 0.7, the mean of the leg length is 16cm, with a standard deviation of 2cm, and the mean jumping distance is 20cm, with a standard deviation of 5cm. The equation for the least squares regression line of jumping distance on leg length is

Jumping distance = -8+ 1.75 (Leg length)

A correct statement about the variables is

The collapsing variable is airport location.

The stem and leaf plot below summarizes the final year averages of a graduating honors class in the Dedman College. Select the correct statement.

The maximum score is 94.

Which of the following statements is always true?

The sample standard deviation is a measure of variation around the sample mean.

We are interested in predicting how far a frog can jump (measured in cm), based on it's leg length (also in cm). We collect data on 50 frogs, allowing each frog one leap. We find the correlation, r is 0.7, the mean of the leg length is 16cm, with a standard deviation of 2cm, and the mean jumping distance is 20cm, with a standard deviation of 5cm. The predicted distance jumped by a frog of leg length 4cm is -1cm. The best explanation of this is

The straight line relationship should not be extrapolated for such small frogs

If two variables are positively correlated, the regression line must have a positive slope.

True

Simpson's paradox concerns 3 categorical variables.

True

The correlation coefficient (r) does not depend on the units of measurement.

True

f the data are normally distributed, 68% of the data are within one standard deviation of the mean.

True

The correct conclusion to draw here is

Yes, airline AB was slightly more on time overall, but it is because it mostly had passengers leaving from Phoenix, and airline AS mostly had passengers leaving from Seattle.