Bicycling, the world's leading cycling magazine, reviews hundreds of bicycles throughout the year. Their "Road-Race" category contains reviews of bikes used by riders primarily interested in racing. One of the most important factors in selecting a bike for racing is the weight of the bike. The following data show the weight (pounds) and price ($) for 10 racing bikes reviewed by the magazine.†

(a)

Use the data to develop an estimated regression equation that could be used to estimate the price for a bike given the weight. (Round your numerical values to the nearest integer).

ŷ =

(b)

Compute

r².

(Round your answer to three decimal places.)

r²

=

Did the estimated regression equation provide a good fit?

The estimated regression equation provided a good fit, since r² ≥ 0.55.The estimated regression equation did not provide a good fit, since r² < 0.55.     The estimated regression equation provided a good fit, since r² < 0.55.The estimated regression equation did not provide a good fit, since r² ≥ 0.55.

(c)

Predict the price (in dollars) for a bike that weighs 13 pounds. (Round your answer to the nearest dollar.)

$

Question 2 There are 6 cities in Kilroy County.  The county must determine where to build central fire stations.  The county wants to build the minimum number of central fire stations needed to ensure that at least two fire stations are within 20 minutes (driving time) of each city. The times (in minutes) required to drive between the cities in Kilroy County are given in the table. Formulate a model that will tell Kilroy how many fire stations should be built and where they should be located.

Decision variables (1 mark):

Objective function (1 mark):

Constraints :

Additional constraint :Either City 1 or City 2 (or both) must be selected to build a fire station in if both City 3 and City 4 are selected to build fire stations in.

1) The mean lifetime of a tire is 36 months with a variance of 49. If 126 tires are sampled, what is the probability that the mean of the sample would differ from the population mean by greater than 0.44 months? Round your answer to four decimal places.

2) Suppose that a study of elementary school students reports that the mean age at which children begin reading is 5.5 years with a standard deviation of 1.1 years.

a) If a sampling distribution is created using samples of the ages at which 47 children begin reading, what would be the mean of the sampling distribution of sample means? Round to two decimal places, if necessary.

b) If a sampling distribution is created using samples of the ages at which 47 children begin reading, what would be the standard deviation of the sampling distribution of sample means? Round to two decimal places, if necessary.

3) A production manager at a wall clock company wants to test their new wall clocks. The designer claims they have a mean life of 15 years with a variance of 25. If the claim is true, in a sample of 41 wall clocks, what is the probability that the mean clock life would be less than 15.4 years? Round your answer to four decimal places.

After examining these data for all the jurisdictions, someone notes that certain areas have an unusually high “percent of 18-64 yr-olds with no high school diploma.” Based on this finding, this individual concludes that the high percentages are due to the rising population of immigrants in those areas. Further, the individual argues that any estimates of the associated “percent of low-income working families” in those areas should be recalculated after removing this sub-population from the data set, as they are causing the area to “look bad”. In addition to thinking critically, use the key rules about linear regression and extrapolation to write a statistically appropriate and socially responsible response to the individual’s conclusion and argument.

Nigel Rex, Remski Catsakoff and Rudolfo, are back with another logic problem. Using the variables as indicated below, translate the following English sentences into propositions and then provide a formal proof to show the conclusion: Nigel does not play with Rudolfo. Remski is calm or Rudy is not thin. If Nigel is not short or Rudolfo is thin, then Rudolfo dislikes corn. If Nigel is short then he plays with Rudolfo. If Nigel is not short or Rudolfo dislikes corn then Remski is not calm. Use a formal argument to show that Rudolfo is not thin.

variable means

16. p Nigel is short

17. q Rudolfo is thin

18. r Rudolfo dislikes corn

19. s Remski is calm

20. t Nigel plays with Rudolfo

An economist wants to estimate the mean per capita income (in thousands of dollars) for a major city in California. Suppose that the mean income is found to be $23.1 for a random sample of 3231 people. Assume the population standard deviation is known to be $11.8. Construct the 95% confidence interval for the mean per capita income in thousands of dollars. Round your answers to one decimal place.

Define the stochastic process  where . Find   

The monthly expenditures on food by single adults living in one neighborhood of Los Angeles are normally distributed with a mean of $410 and a standard deviation of $75. Determine the percentage of samples of size 9 that have mean expenditures within $20 of the population mean expenditure of $410.

1) what's the probability that someone else has the same birthday as you (assuming neither has a birthday in a leap year).

2) what's the probability that someone in a room of 20 people that one them has the same birthday as you (also assuming neither has a birthday in a leap year).

3) what's the probability that someone in a room of 20 people that there will be 3 people that have the same birthday (assuming none have a birthday in a leap year).

1. In a presidential election, 308 out of 611 voters surveyed said that they voted for the candidate who won. Use a 0.01 significance level to test that among all voters, the percentage who believe they voted for the winning candidate is different from 43%, which is the actual percentage of votes for the winning candidate. What does the result suggest about voter perceptions? Must show all work.

You have been asked to conduct a study related to consumer loyalty toward three different retail formats (i.e., department stores, specialty stores, and off-price retailers). After gathering background information, you decide to focus your study on three research streams; retail service quality, consumer satisfaction, and consumer loyalty. The literature suggests that there are five dimensions of retail service quality; physical aspect, reliability, personal interaction, problem solving, and policy. In addition, you are interested in identifying factors (i.e., retail service quality) that may contribute to consumer satisfaction and consumer loyalty toward these retailers. According to the literature, consumer satisfaction is a unidimensional construct and consumer loyalty consists of two dimensions; word-of-mouth and behavioral intention

State the null hypothesis and the alternative hypothesis

What are the dependent and independent variables

What statistical test would you run in SPSS

In Canada, do young males (Y) weigh more than older males (O) on average? To investigate this question, weights of eighteen males randomly selected from each group were recorded. Summary statistics are given in the following table. Assume weight of each group follows a normal distribution. (If you think the samples are independent, then assume equal variances.)

What will be the respective degrees of freedom and the P-value range for testing if young Canadian males weigh more than older males on average?

Twelve inspectors, each using two different kinds of calipers, measured the diameter of a ball bearing. Summary statistics are given in the following table. Assume both samples come from normal distributions. (If you think the samples are independent, then assume equal variances.)

What is the margin of error for a 95% confidence interval for the difference in mean diameter measurements for the two kinds of calipers?

Twelve inspectors, each using two different kinds of calipers, measured the diameter of a ball bearing. Summary statistics are given in the following table. Assume both samples come from normal distributions. (If you think the samples are independent, then assume equal variances.)

Is there a difference in mean diameter measurements for the two kinds of calipers? In performing this hypothesis test, what is the P-value range based on the t-table and the conclusion at the 1% significance level?

In order to determine whether there was a difference in the survival rate between females and males, a two-sample proportion test was applied. The following is the output for the test with some entries missing:

Two sample proportion hypothesis test:
p₁ : Proportion of successes (Success = Survived) for Survival where Gender=Female
p₂ : Proportion of successes (Success = Survived) for Survival where Gender=Male
p₁ - p₂ : Difference in proportions
H₀ : p₁ - p₂ = 0
H_A : p₁ - p₂ ≠ 0

Hypothesis test results:

What is the appropriate conclusion at the 1% significance level based off this data?

Select one:

a. Since P-value < α, reject H₀ and there is sufficient evidence of a difference in survival rate between males and females.

b. Since P-value > α, reject H₀ and there is sufficient evidence of a difference in survival rate between males and females.

c. Since P-value < α, do not reject H₀ and there is insufficient evidence of a difference in survival rate between males and females.

d. Since P-value > α, do not reject H₀ and there is insufficient evidence of a difference in survival rate between males and females.

e. Since P-value > α, do not reject H₀ and there is sufficient evidence of equality in survival rate between males and females.

The company who makes Chips Ahoy cookies states that there is an average of 23 chocolate chips per cookie. You take a sample of cookies and count the chips. For your sample of 30 cookies, the average # of chips in the cookies is 23.6 chips with a standard deviation of 2 chips. Use this data to test the claim that the company makes. Use a 95% significance level but you may use a two tailed OR a one tailed test. You decide. Does your hypothesis test support the claim that Chip Ahoy is making?

Provide a 95% confidence interval to estimate the true number of chips in Chips Ahoy cookies. Does your interval support the claim of the company?

In a random sample of 480 males, it was found that 14.4% write with their left hand. In a random sample of 1040 females, it was found that 9.6% write with their left hand. We want to use a 95% significance level to test the claim that the rate of left-handedness among females is less than that among males. Provide a hypothesis test with all six steps AND use a p-value to make your decision.