1. The City of Blueville has implemented Red Light Camera Program for one year and the City Manager wants to evaluate the effectiveness of program. After reviewing the traffic accident reports in the past several decades years, Assistant City Manager found that there were average of 115 accidents each year, normally distributed with standard deviation of 25. There were 100 accidents during the first year.

1. Test the (alternative) hypothesis that the number of accidents was reduced significantly at 0.05 significance level. (10 points)

Calculate 95% confidence interval, and what will be your conclusion? Explain why you reach or do not reach the same conclusion as in question (a).

Uniform Distribution

You believe stock price will follow uniform distribution with mean of 100 and MAD 20. You are pricing a CALL option with strike at 110.

a. what is the range of the distribution?

b. what is the probability that the call will be ITM at expiration (ie stock price ends above strike at 110)?

c. what is the conditional mean of stock price when CALL is ITM (aka stock price is above strike 110)?

d. what is the conditional CALL option average payment when the CALL is ITM?

e. what is the fair value of the CALL today, ie the unconditional average payment today?

(additional practice: redo for 90 strike CALL, 90 strike PUT, 110 strike PUT)

A statistical program is recommended.

The owner of a movie theater company would like to predict weekly gross revenue as a function of advertising expenditures. Historical data for a sample of eight weeks follow.

(a) Use α = 0.01 to test the hypotheses

for the model y = β₀ + β₁x₁ + β₂x₂ + ε,  where

Find the value of the test statistic. (Round your answer to two decimal places.)

Use α = 0.05 to test the significance of β₁.

Find the value of the test statistic. (Round your answer to two decimal places.)

Use α = 0.05 to test the significance of β₂.

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =

1. Provide an appropriate response.
   
   A district administrator wants to determine the effect of truancy on academic achievement. She asks the dean at a high school to randomly select the records of 50 truant students and to randomly select the records of 50 nontruant students. Identify any problems that are likely to cause confounding.

   		the use of records from only one school
   		nothing (this is a well-designed retrospective study)
   		the use of one person to select the records for members of both groups
   		the number of records in each group (since, presumably, there are more nontruant students, there should be more members selected from that group)

2 points

Question 40

1. Identify which of these types of sampling is used: random, stratified, systematic, cluster, convenience.
   
   To avoid working late, a quality control analyst simply inspects the first 100 items produced in a day.

   		Random
   		Convenience
   		Cluster
   		Stratified
   		Systematic

2 points

Question 41

1. Construct the requested table. Round relative frequencies to the nearest hundredth of a percent, unless otherwise indicated.
   
   The following data show the body temperatures (°F) of randomly selected subjects. Construct a relative frequency table with seven classes: 96.9 - 97.2, 97.3 - 97.6, 97.7 - 98.0, and so on.
   
   Round relative frequencies to the nearest tenth of a percent.

2 points

Question 42

1. Construct the requested table.
   
   The following data represent the total number of years of formal education for 40 employees of a bank.
   
   
   
   Create a frequency table for the number of years of education.

2 points

Question 43

1. Determine whether the evaluated group is a population or a sample.
   
   A researcher determines that 42.7% of all downtown office buildings have ventilation problems.

   		Population
   		Sample

2 points

Question 44

1. Determine whether the evaluated group is a population or a sample.
   
   A researcher examines the records of all the registered voters in one city and finds that 43% are registered Democrats.

   		Sample
   		Population

2 points

Question 45

1. Provide a written description of the complement of the given event.
   
   Of ten adults, at least one of them has high blood pressure.

   		None of the adults have high blood pressure.
   		At most one of the adults has high blood pressure.
   		All of the adults have high blood pressure.
   		Nine of the adults have high blood pressure.

2 points

Question 46

1. Provide a written description of the complement of the given event.
   
   When several textbooks are edited, none of them are found to be free of errors.

   		All of the textbooks are free of errors.
   		One of the textbooks is free of errors.
   		At least one of the textbooks is free of errors.
   		At most one of the textbooks is free of errors.

2 points

Question 47

1. Find the variance for the given data. Round your answer to one more decimal place than the original data. To get the best deal on a microwave oven, Jeremy called six appliance stores and asked the cost of a specific model. The prices he was quoted are listed below:
   

   $663

   $273

   $410

   $622

   $174

   $374

   		36,838.3 dollars2
   		1,207,582.7 dollars2
   		30,698.6 dollars2
   		36,838.2 dollars2

2 points

Question 48

1. Find the standard deviation for the given data. Round your answer to one more decimal place than the original data.
   
   The numbers listed below represent the amount of precipitation (in inches) last year in six different U.S. cities.

   17.2​

   16.6​

   30.8​

   28.6​

   20.3​

   18.4

   		6.15 in.
   		3088.7 in.
   		2899.6 in.
   		29.7 in.

2 points

Question 49

1. Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard deviations. That is, unusual values are either less than μ - 2σ or greater than μ + 2σ.
   
   A survey for brand recognition is done and it is determined that 68% of consumers have heard of Dull Computer Company. A survey of 800 randomly selected consumers is to be conducted. For such groups of 800, would it be unusual to get 504 consumers who recognize the Dull Computer Company name?

   		Yes
   		No

2 points

Question 50

1. Find the standard deviation, σ, for the binomial distribution which has the stated values of n and p. Round your answer to the nearest hundredth.
   
   n = 1617; p = 0.57

   		σ = 17.50
   		σ = 24.03
   		σ = 23.18
   		σ = 19.91

The following estimated regression equation based on 10 observations was presented.

ŷ = 25.1670 + 0.5705x₁ + 0.4960x₂

Here, SST = 6,732.125, SSR = 6,221.375, s_b1 = 0.0818,  and  s_b2 = 0.0561.

a) Compute MSR and MSE. (Round your answers to three decimal places.)

MSR=

MSE=

Find the value of the test statistic. (Round your answer to two decimal places.)

F =

Perform a t test for the significance of β₁. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

t =

Perform a t test for the significance of β₂. Use α = 0.05.

Find the value of the test statistic. (Round your answer to two decimal places.)

t =

Consider the following information, which are estimates as of mid-2019.

Consider the following information, which are estimates as of mid-2019.

For each country listed above, calculate r and how many people there will be in mid-2020 if population growth is exponential. Use the differential equation (dN/dt) for exponential population growth that was presented in Lecture.

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

1. The estimated regression equation for this data is  ŷ = 21.990 + 0.330x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

1a. State the null and alternative hypotheses.

(a) H₀: β₀ ≠ 0
H_a: β₀ = 0

(b) H₀: β₁ = 0
H_a: β₁ ≠ 0    

(c) H₀: β₁ ≠ 0
H_a: β₁ = 0

(d) H₀: β₀ = 0
H_a: β₀ ≠ 0

(e) H₀: β₁ ≥ 0
H_a: β₁ < 0

1b. Find the value of the test statistic. (Round your answer to three decimal places.)

1c. Find the p-value. (Round your answer to four decimal places.)

p-value =

1d. What is your conclusion?

(a) Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b) Reject H₀. We conclude that the relationship between price ($) and overall score is significant.     

(c) Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(d) Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

2. Test for a significant relationship using the F test. Use α = 0.05.

2a. State the null and alternative hypotheses.

(a) H₀: β₁ = 0
H_a: β₁ ≠ 0

(b) H₀: β₀ = 0
H_a: β₀ ≠ 0    

(c) H₀: β₁ ≠ 0
H_a: β₁ = 0

(d) H₀: β₀ ≠ 0
H_a: β₀ = 0

(e) H₀: β₁ ≥ 0
H_a: β₁ < 0

2b. Find the value of the test statistic. (Round your answer to two decimal places.)

2c. Find the p-value. (Round your answer to three decimal places.)

p-value =

2d. What is your conclusion?

(a) Do not reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(b) Reject H₀. We conclude that the relationship between price ($) and overall score is significant.    

(c) Reject H₀. We cannot conclude that the relationship between price ($) and overall score is significant.

(d) Do not reject H₀. We conclude that the relationship between price ($) and overall score is significant.

3,. Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

A widget company tested 101,000 widgets, of which only 1,000 had defects. The company’s test correctly identified defects 99% of the time and correctly identified non-defects 95% of the time. 2 (a) What percentage of the widgets marked as defects were actually defective? (b) What percentage of the widgets marked as non-defects were not defective? (c) The answer to problem a is counter-intuitive. Explain what happened? (d) What would be your suggestion for improving the accuracy of the defect/nondefect identification. Improving the accuracy of the tests is not a valid answer.

Why would you want to use the Monte Carlo Simulation to explore a decision option rather than solve the branch analytically?

A distribution is normal with a mean of 25 and a standard deviation of 3.

11. What is the median of the distribution?

12. What percent of the distribution lies between 22 and 28?

13. What percent of the distribution lies below 16?

14. What percent of the distribution lies above 28?

First, sort the data.

Second, build a GFDT for this table with a classwidth of 5.
(Be sure your lower class limits are multiples of the classwidth.)
Next, answer the following questions about the data set:
1. What is the first lower class limit in your GFDT (given the classwidth of 5)?
2. Express the third class as a closed interval, i.e., [a,b][a,b].
3. Give the frequency for the third class.
4. What is the (arithmetic) mean for this data (report accurate to one decimal place)?
5. Using the GFDT, what is the mode for this data set (use the appropriate definition for mode)?(take the class with the biggest frequency [40,44], and apply the following formula (Lower class limit+Upper class limit)/2
6. What is the standard deviation for this data (report accurate to two decimal places)?
7. What is the five number summary for this data set (separate numbers with a comma)?
8. What is the IQR?
9. What usual score (i.e., non-outlier) has the largest positive z-score less than z=2z=2? (Give the data value, not the z-score.)
10. Give the fences---this would suggest something other than z-scores---for the mild outliers at the maximal end of the data set; report as a closed interval, i.e., [upper mild fence, upper extreme fence].

Need help with solving this problem, please dummy it down for me I would also like to know how to solve it. Please provide answers thanks!

Consider the following data on price ($) and the overall score for six stereo headphones tested by a certain magazine. The overall score is based on sound quality and effectiveness of ambient noise reduction. Scores range from 0 (lowest) to 100 (highest).

(a) The estimated regression equation for this data is  ŷ = 24.799 + 0.302x, where x = price ($) and y = overall score. Does the t test indicate a significant relationship between price and the overall score? Use α = 0.05.

State the null and alternative hypotheses.

H₀: β₁ = 0
H_a: β₁ ≠ 0

H₀: β₀ ≠ 0
H_a: β₀ = 0

H₀: β₁ ≠ 0
H_a: β₁ = 0

H₀: β₁ ≥ 0
H_a: β₁ < 0

H₀: β₀ = 0
H_a: β₀ ≠ 0

Find the value of the test statistic. (Round your answer to three decimal places.)

Find the p-value. (Round your answer to four decimal places.)

p-value =

Find the value of the test statistic. (Round your answer to two decimal places.)

Find the p-value. (Round your answer to three decimal places.)

p-value =  

(c) Show the ANOVA table for these data. (Round your p-value to three decimal places and all other values to two decimal places.)

The grades of a sample of 10 applicants, selected at random from a large population, are 71, 86, 75, 63, 92, 70, 81, 59, 80, and 90. Compute the sample variance. Can we infer at the 90% confidence that the population variance is significantly less than 100? (i.e. Perform Hypothesis testing)

1) An assumption of non parametric tests is that the distribution must be normal: (a) True (b) False

2) ​One characteristic of the chi-square tests is that they can be used when the data are measured on a nominal scale: (a) True (b) False

3) Which of the following accurately describes the observed frequencies for a chi-square test?​: (a) They are always whole numbers. (b) ​They can contain fractions or decimal values. (c) They can contain both positive and negative values. (d) ​They are always the same value.

4) The term expected frequencies refers to the frequencies ____.​ (a) ​found in the sample data (b) ​found in the population being examined (c) ​computed from the null hypothesis (d) ​that are hypothesized for the population being examined

5) For a given alpha level, what happens to the critical value for a chi-square test if the number of categories is increased?​: (a) The critical value also increases. (b) The critical value decreases. (c) ​The critical value depends on the sample size, not the number of categories. (d) ​the critical value is determined entirely by the alpha level.

6) A chi-square test for independence has df = 3. What is the total number of categories (cells in the matrix) that were used to classify individuals in the sample?​: (a) ​four (b) ​six (c) ​eight (d) nine

7) Suppose we wanted to explore the following research question: Are males more likely to choose a business course than females? Which groups are being compared here?

(a)Males and Females (b) Students enrolled in Business, Social Science and Other courses