Q: A frequency table for grades is constructed. Which formula is used to calculate the relative frequency for grade A?

$$\text{Relative Frequency} = \frac{\text{Frequency of A}}{\text{Total number of students}}$$

Question 1

A teacher records the letter grades of her 15 students: A, A, B, C, A, B, C, B, A, A, A, C, A, D, A. What is the level of measurement for the variable 'letter grade'?

Accepted Answer

Nominal

Question 2

Given the grade data: A, A, B, C, A, B, C, B, A, A, A, C, A, D, A. What is the median grade?

Accepted Answer

A

Question 3

In the teacher's study of her class grades, what is the population?

Accepted Answer

All students in her course

Question 4

Is the relative frequency of A grades in the teacher’s course a statistic or a parameter? Why?

Accepted Answer

Parameter, because it describes the entire population of her class

Question 5

Is there any sampling error in the teacher’s study of her class grades?

Accepted Answer

No, because the entire population was measured

Question 6

Scientists collected data on Lyme disease cases and drowning deaths for each month in a rural county. Is this an observational study or a designed experiment?

Accepted Answer

Observational study

Question 7

In the Lyme disease study, which is the explanatory variable and which is the response variable?

Accepted Answer

Explanatory: Month; Response: Cases of Lyme disease

Question 8

Why is 'month' a confounding variable in the Lyme disease and drowning deaths study?

Accepted Answer

Because both Lyme disease cases and drowning deaths vary by month, making it difficult to determine if one causes the other

Question 9

Given the Lyme disease cases per month: 3, 2, 2, 4, 5, 16, 23, 13, 6, 5, 4, 1. What is the population mean number of cases? Use the formula $$\bar{x} = \frac{\sum x_i}{n}.$$

Accepted Answer

$$\bar{x} = \frac{84}{12} = 7$$

Question 10

Calculate the population standard deviation for the Lyme disease cases using $$\sigma = \sqrt{\frac{\sum (x_i - \mu)^2$}{N}}. If $$the sum of squared deviations is 510, what is $$\sigma$$?

Accepted Answer

$$\sigma = \sqrt{\frac{510}{12}} \approx 6.52$$

Question 11

Given $$\bar{y} = 3.7$$, $$s_y = 4.4$$, and $$r = 0.96$$, and $$\bar{x} = 7$$, $$s_x = 6.52$$, what is the equation of the least squares regression line for predicting drowning deaths from Lyme disease cases? Use $$y = a + bx$$, where $$b = r \frac{s_y}{s_x}$$ and $$a = \bar{y} - b\bar{x}.$$

Accepted Answer

$$y = 0.65x + -0.86$$

Question 12

In July of the next year, there were 40 cases of Lyme disease. In December, there were 2 cases. Why might it be acceptable to use the regression line to estimate drowning deaths in December but not July?

Accepted Answer

Because 2 cases is within the range of the original data, but 40 cases is an extrapolation far outside the observed range

Question 13

A frequency table for grades is constructed. Which formula is used to calculate the relative frequency for grade A?

Accepted Answer

$$	ext{Relative Frequency} = \frac{	ext{Frequency of A}}{	ext{Total number of students}}$$

Question 14

If a study records every member of a population, which of the following is true?

Accepted Answer

There is no sampling error

Question 15

Which of the following best describes a confounding variable?

Accepted Answer

A variable that influences both the explanatory and response variables, making it difficult to determine causality

Question 16

If the correlation coefficient $$r$$ between Lyme disease cases and drowning deaths is 0.96, what does this indicate?

Accepted Answer

There is a strong positive linear relationship between the two variables

Question 17

Which formula is used to calculate the population mean for a dataset $$x_1$$, $$x_2$$, ..., x_n$$?

Accepted Answer

$$\bar{x} = \frac{\sum_{i=1}^n x_i}{n}$$

Question 18

Which formula is used to calculate the population standard deviation for a dataset $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\mu$$?

Accepted Answer

$$\sigma = \sqrt{\frac{\sum_{i=1}^n (x_i - \mu)^2$}{n}}$$

MA 113 Alternate Midterm 1: Statistics Study Guidance

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