eBook Almost all U.S. light-rail systems use electric cars that run on tracks built at street level. The Federal Transit Administration claims light-rail is one of the safest modes of travel, with an accident rate of .99 accidents per million passenger miles as compared to 2.29 for buses. The following data show the miles of track and the weekday ridership in thousands of passengers for six light-rail systems.

Dylan Jones kept careful records of the fuel efficiency of his new car. After the first twelve times he filled up the tank, he found the mean was 22.9 miles per gallon (mpg) with a sample standard deviation of 1.2 mpg.

1. Compute the 98% confidence interval for his mpg. (Use t Distribution Table.) (Round your answers to 3 decimal places.)

2. How many times should he fill his gas tank to obtain a margin of error below 0.15 mpg? (Use z Distribution Table.) (Round your answer to the next whole number.)

A study is performed in a large southern town to determine whether the average amount spent on fod per four person family in the town is significantly different from the national average. Assume the national average amount spent on food for a four- person family is $150.

A what is the null and alternative hypothesis?

b. Is the sample evidence significant? significance level?

A.) A manufacturer knows that their items have a normally distributed lifespan, with a mean of 6.9 years, and standard deviation of 1 years. If you randomly purchase one item, what is the probability it will last longer than 9 years?

B.) A particular fruit's weights are normally distributed, with a mean of 784 grams and a standard deviation of 24 grams. If you pick one fruit at random, what is the probability that it will weigh between 845 grams and 859 grams.

C.) A particular fruit's weights are normally distributed, with a mean of 615 grams and a standard deviation of 11 grams. The heaviest 19% of fruits weigh more than how many grams?
Give your answer to the nearest gram.

D.) A distribution of values is normal with a mean of 228.7 and a standard deviation of 33.7. Find P₈₅, which is the score separating the bottom 85% from the top 15%.
P₈₅ =

Enter your answer as a number accurate to 1 decimal place. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

E.) The combined SAT scores for the students at a local high school are normally distributed with a mean of 1470 and a standard deviation of 303. The local college includes a minimum score of 2137 in its admission requirements.
What percentage of students from this school earn scores that satisfy the admission requirement?
P(X > 2137) = %
Enter your answer as a percent accurate to 1 decimal place (do not enter the "%" sign). Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.

7.16 How do you position yourself when you are going to sleep? A website tells us that 41% of use start in the fetal position, another 28% start on our side with legs straight, 13% start on their back, and 7% on their stomach. The remaining 11% have no standard starting sleep position. If a random sample of 1000 people produces the frequencies in the table below, should you doubt the proportions given in the article in the website? Show all the details of the test, and use a 5% significance level.

Slices of pizza for a certain brand of pizza have a mass that is approximately normally distributed with a mean of 67.1 grams and a standard deviation of 2.2 grams. a) For samples of size 12 pizza slices, what is the standard deviation for the sampling distribution of the sample mean? State answer to five decimal places. b) What is the probability of finding a random slice of pizza with a mass of less than 66.5 grams? State the answer to four decimal places. c) What is the probability of finding a 12 random slices of pizza with a mean mass of less than 66.5 grams? State the answer to four decimal places. d) What sample mean (for a sample of size 12) would represent the bottom 15% (the 15th percentile)? State answer to one decimal place. grams

A study conducted by Stanford researchers asked children in two elementary schools in San Jose, CA to keep track of how much television they watch per week. The sample consisted of 198 children. The mean time spent watching television per week in the sample was 15.41 hours with a standard deviation of 14.16 hours.

(a) Carry out a one-sample t-test to determine whether there is convincing evidence that average amount of television watching per week among San Jose elementary children exceeds fourteen hours per week. (Report the hypotheses, test statistic, p-value, and conclusion at the 0.10 level of significance.)

(b) Calculate and interpret a one-sample 90% t-confidence interval for the population mean.

(c) Comment on whether the technical conditions for the t-procedures are satisfied here. [Hint: What can you say based on the summary statistics provided about the likely shape of the population?]

2.In a test of the hypothesis H0: μ = 50 versus Ha: μ < 50, a sample of 40 observations is selected from a normal population and has a mean of 49.0 and a standard deviation of 4.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would reject H0.

3.In a test of the hypothesis H0: μ = 10 versus Ha: μ≠ 10, a sample of 16 observations possessed mean 11.4 and standard deviation 3.1.

a) Find the P-value for this test.

b) Give all values of the level of significance α for which you would not reject H0.

What is a linear regression analysis? What does it provide you? Your answer should address development of a linear response equation and associated uncertainty in prediction.

Suppose we have a binomial experiment in which success is defined to be a particular quality or attribute that interests us.

(a)

• Suppose n = 36 and
• p = 0.39.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

(b)

Suppose

• n = 25 and
• p = 0.15.

Can we safely approximate p̂ by a normal distribution? Why or why not? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)

(c)

Suppose

• n = 46 and
• p = 0.33.

(For each answer, enter a number. Use 2 decimal places.)
n·p =
n·q =

Can we approximate p̂ by a normal distribution? Why? (Fill in the blank. There are four answer blanks. A blank is represented by _____.)

_____, p̂ _____ be approximated by a normal random variable because _____ _____.

first blank

YesNo    

second blank

cancannot    

third blank

both n·p and n·q exceedn·p exceeds    n·p and n·q do not exceedn·q does not exceedn·p does not exceedn·q exceeds

fourth blank (Enter an exact number.)


What are the values of μ_p̂ and σ_p̂? (For each answer, enter a number. Use 3 decimal places.)
μ_p̂ = mu sub p hat =

σ_p̂ = sigma sub p hat =

The data set airquality is one of R’s included data sets. It shows daily measurements of ozone concentration (Ozone), solar radiation (Solar.R), wind speed (Wind), and temperature (Temp) for 5 summer months in 1977 in New York City. Some of the observations are missing and are recorded as NA, meaning not available. View an overall summary of the variables in airquality with the command

> summary(airquality) Ignore the summaries for Month and Day since those variables should be factors, not numeric variables, and their summaries are meaningless. Attach airquality to your workspace

> attach(airquality) and make boxplots of Ozone, Solar.R, Wind, and Temp. Comment on any noteworthy features.

Write a few sentences comparing bivariate correlation and bivariate regression. You need to discuss when it is appropriate to use each of these statistics.

Suppose Y is an random variable. If P(a<Y<2a)=0.16 and the median of Y is 5, what is a? Note: There may be more than one solution. Report all.

1. The Coefficient of Determination is *

a. the percent of variance in the dependent variable that can be explained by the independent variable

b. the ratio of the variance of Y to the variance of Y for a specific X

c. a measure of how strong the linear relationship is between the explanatory and response variables

2.

The null hypothesis for a regression model is state as *

a. beta_1=0: there is no relationship

b. beta_1 > 0: there is a positive relationship

c. rho=0: there is no relationship

d. rho < 1: there is a negative relationship

3.Choose the best interpretation of \beta_{0} *

a. the sample correlation between x and y

b. the change in y as x increases by 1 unit

c. the amount of uncertainty remaining after fitting the model

d. the value of y when all x's are zero

4.Linear regression analysis is used to assess the relationship between what two types of measurements? *

a. quantiative; quantitative

b. categorical; categorical

c. quantitative; categorical

1. Explain in words what a confidence interval means to someone who has never taken statistics.

2. There is concern that rural Minnesota is aging at a different rate than urban Minnesota. We want to test if the average age in rural Minnesota is different from the average age in urban Minnesota. Write out the null and alternative hypotheses.

3. At the 5% significance level, do you reject the null hypothesis? Why? Explain this to someone who has never taken statistics.