The U.S. Department of Transportation provides the number of miles that residents of the 75 largest metropolitan areas travel per day in a car. Suppose that for a simple random sample of 50 Buffalo residents the mean is $22.5$ miles a day and the standard deviation is $8.4$ miles a day, and for an independent simple random sample of 40 Boston residents the mean is $18.6$ miles a day and the standard deviation is $7.4$ miles a day.

What is the point estimate of the difference between the mean number of miles that Buffalo residents travel per day and the mean number of miles that Boston residents travel per day?

What is the $95 \%$ confidence interval for the difference between the two population means?

The following results are for independent random samples taken from two populations.

$$\begin{array} { l l } { \text { Sample } 1 } & { \text { Sample } 2 } \\ { n _ { 1 } = 20 } & { n _ { 2 } = 30 } \\ { \overline { x } _ { 1 } = 22.5 } & { \overline { x } _ { 2 } = 20.1 } \\ { s _ { 1 } = 2.5 } & { s _ { 2 } = 4.8 } \end{array}$$

What is the degrees of freedom for the t distribution?

The following results come from two independent random samples taken of two populations.

$$\begin{array} { l l } { \text { Sample } 1 } & { \text { Sample } 2 } \\ { n _ { 1 } = 50 } & { n _ { 2 } = 35 } \\ { \overline { x } _ { 1 } = 13.6 } & { \overline { x } _ { 2 } = 11.6 } \\ { \sigma _ { 1 } = 2.2 } & { \sigma _ { 2 } = 3.0 } \end{array}$$

Provide a 95% confidence interval for the difference between the two population means.

The following results are for independent random samples taken from two populations.

$$\begin{array} { l l } { \text { Sample } 1 } & { \text { Sample } 2 } \\ { n _ { 1 } = 20 } & { n _ { 2 } = 30 } \\ { \overline { x } _ { 1 } = 22.5 } & { \overline { x } _ { 2 } = 20.1 } \\ { s _ { 1 } = 2.5 } & { s _ { 2 } = 4.8 } \end{array}$$

At 95% confidence, what is the margin of error?

The following results come from two independent random samples taken of two populations.

$$\begin{array} { l l } { \text { Sample } 1 } & { \text { Sample } 2 } \\ { n _ { 1 } = 50 } & { n _ { 2 } = 35 } \\ { \overline { x } _ { 1 } = 13.6 } & { \overline { x } _ { 2 } = 11.6 } \\ { \sigma _ { 1 } = 2.2 } & { \sigma _ { 2 } = 3.0 } \end{array}$$

What is the point estimate of the difference between the two population means?

Consider the following data for two independent random samples taken from two normal populations.

$$\begin{matrix} \text{Sample 1 |} & \text{10} & \text{7} & \text{13} & \text{7} & \text{9} & \text{8}\\ \text{Sample 2 |} & \text{8} & \text{7} & \text{8} & \text{4} & \text{6} & \text{9}\\ \end{matrix}$$

Compute the two sample standard deviations.

The average expenditure on Valentine’s Day was expected to be $100.89 (USA Today, February 13, 2006). Do male and female consumers differ in the amounts they spend? The average expenditure in a sample survey of 40 male consumers was$135.67, and the average expenditure in a sample survey of 30 female consumers was $68.64. Based on past surveys, the standard deviation for male consumers is assumed to be$35, and the standard deviation for female consumers is assumed to be $20.

What is the point estimate of the difference between the population mean expenditure for males and the population mean expenditure for females?

Consider the following data for two independent random samples taken from two normal populations.

$$\begin{matrix} \text{Sample 1 |} & \text{10} & \text{7} & \text{13} & \text{7} & \text{9} & \text{8}\\ \text{Sample 2 |} & \text{8} & \text{7} & \text{8} & \text{4} & \text{6} & \text{9}\\ \end{matrix}$$

What is the point estimate of the difference between the two population means?

Consider the following data for two independent random samples taken from two normal populations.

$$\begin{matrix} \text{Sample 1 |} & \text{10} & \text{7} & \text{13} & \text{7} & \text{9} & \text{8}\\ \text{Sample 2 |} & \text{8} & \text{7} & \text{8} & \text{4} & \text{6} & \text{9}\\ \end{matrix}$$

Compute the two sample means.

Consider the following data for two independent random samples taken from two normal populations.

$$\begin{matrix} \text{Sample 1 |} & \text{10} & \text{7} & \text{13} & \text{7} & \text{9} & \text{8}\\ \text{Sample 2 |} & \text{8} & \text{7} & \text{8} & \text{4} & \text{6} & \text{9}\\ \end{matrix}$$

What is the 90% confidence interval estimate of the difference between the two population means?

The national average for the math portion of the College Board’s Scholastic Aptitude Test (SAT) is 515 (The World Almanac, 2009). The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores.

a. What percentage of students have an SAT verbal score greater than 615? b. What percentage of students have an SAT verbal score greater than 715? c. What percentage of students have an SAT verbal score between 415 and 515? d. What percentage of students have an SAT verbal score between 315 and 615?

The national average for the verbal portion of the College Board’s Scholastic Aptitude Test (SAT) is 507 (The World Almanac, 2006). The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores. $\newline$ What percentage of students have an SAT verbal score between 407 and 507?

In 2006, the Scholastic Aptitude Test (SAT) math scores for college-bound seniors roughly followed a normal distribution

$$y=0.0035 e^{-(x-518)^2 / 26,450}, \quad 200 \leq x \leq 800$$

where x is the SAT score for mathematics. Find the probability that a senior chosen at random had an SAT score 750 or better. (Source: College Board)

The national average for the verbal portion of the College Board’s Scholastic Aptitude Test (SAT) is 507 (The World Almanac, 2006). The College Board periodically rescales the test scores such that the standard deviation is approximately 100. Answer the following questions using a bell-shaped distribution and the empirical rule for the verbal test scores. $\newline$ What percentage of students have an SAT verbal score greater than 607?