Internet service: An Internet service provider sampled 545 customers, and finds that 65 of them
experienced an interruption in high-speed service during the previous month.

(b) Construct a 99.8% confidence interval for the proportion of all customers who experienced
an interruption. Round the answers to at least three decimal places.

A 99.8% confidence interval for the proportion of all customers who experienced an interruption is
_<p<_.

A tree researcher wishes to test the claim made by a colleague that trees of a certain species in a forest to the north are the same height as the same species in a forest to the south. The researcher collected samples from both forests. In the northern forest, the sample size was 9 trees, the sample average was 32.7 ft, and the sample standard deviation was 6.9 ft. In the southern forest, the sample size was 12 trees, the sample average was 35.4 ft, and the sample standard deviation was 5.6 ft. With alpha = 0.1, test the claim.

Sampling distribution question

1. State the definition of sampling distribution?
2. Let’s assume that we have a Bernoulli random variable X,

X = a with probability 0.78,

X = b with probability 0.22,  

Where a and b are the third and fourth digit of your student number, respectively.(a=9,b=9) Develop a sampling distribution for sample means of the Bernoulli distribution when the sample size is 6

3. What is the expected value of sample means in question 3.b? What is the variance of the sample means?
4. If the sample size increases to a large number n (n is greater than 30), how are the sample means distributed?

1. Explain the process of creating a significance test.

2. How do confidence intervals and significance tests relate?

3. When do you use a matched-pairs t-test?

A researcher conducts an Analysis of Variance (ANOVA) test looking at the effect of different treatment program options (therapy, education and reentry services) and finds that drug use levels vary significantly among between the participants in each of these three groups. For example, the therapy group had lowest amount of drug use (mean=2.0), the education group had the highest (mean=7.0) and the reentry services group was in the middle (mean=6.0). The researcher follows the steps to conduct an ANOVA appropropriately. The researcher's math is correct and she correctly rejects the null. However, she goes on to make the additional conclusion/interpretation: "Therefore, the ANOVA shows that there are statistically significant differences between the therapy group and the reentry services group."

Please evaluate the additional conclusions the researcher makes: a. Is it correct or incorrect to make this additional conclusion using the ANOVA test? Why or why not ? [Note the question is not at all concerned about differences between bivariate and multivariate analysis techniques. It only pertains to understanding ANOVA.]

10) What test should you run to determine if your residuals are not spatially dependent (i.e. they are independent)? If that test proves to be significant, what corrective action can you take?

1. In a sample of 350 students selected from a large college of business, 25% are found to be marketing majors. The 25% is a statistic.

True                 False

2. Lily has been keeping track of what she spends to eat out. The last week's expenditures for meals eaten out were $5.69, $5.95, $6.19, $10.91, $7.49, $14.53, and $7.66. What is the mean amount Lily spends on meals?

__________________

3. Monthly rent in dollars for a sample of 10 stores in a small town in South Dakota are as follows: 220, 216, 220, 205, 210, 240, 195, 235, 204, and 250. What is the sample mean?

__________________

4. Suppose that a firm's sales were $2,500,000 four years ago, and sales have grown annually by 25%, 15%, -5%, and 10% since that time. What was the geometric mean growth rate in sales over the past four years?

                                                                                                __________________

5. The data set 10, 20, 30 has the same variance as the data set 100, 200, 300.

True                 False

6. The values for a sample taken from a particular population are listed below. Calculate the standard deviation for the sample values.

9     14     18     21

                                                __________________

7. A basketball player has the following points for seven games: 20, 25, 32, 18, 19, 22, and 30. Compute the coefficient of variation.

__________________

8. According to the Empirical Rule, if the data form a bell shaped normal distribution, approximately ________ % of the observations will be contained within two standard deviations.

9. In a bell-shaped distribution, there is no difference in the values of the mean, median, and mode.

True                 False

10. A data sample has a mean of 107, a median of 122, and a mode of 134. The distribution of the data is positively skewed.

True                 False

A company owns 400 laptops. Each laptop has an 8% probability of not working. You randomly select 20 laptops for your salespeople. 1.What is the likelihood at most 6 will be broken? 2. What is the likelihood that less than 18 will be broken? 3. What is the likelihood that more than 3 will be broken?

A new design for the braking system on a certain type of car has been proposed. For the current system, the true average braking distance at 40 mph under specified conditions is known to be 120 ft. It is proposed that the new design be implemented only if sample data strongly indicates a reduction in true average braking distance for the new design.

a. Define the parameter of interest.

b. State the relevant hypotheses.

c. Suppose braking distance for the new system is normally distributed with σ = 11. Let ?̅ denote the sample average braking distance for a random sample of 36 observations. Which values of ?̅are more contradictory to H0 than 117.2?

d. What is the P-value in this case? What conclusion is appropriate if α = 0.10?

e. What is the probability that the new design is not implemented when its true average braking distance is actually 115 ft and the test from part (b) is used?

1) Baltimore Furniture Inc. owns two factories, each of which produces three types of tables – the deluxe, medium and the standard. The company has a contract to supply tables to a newly built hotel in downtown Washington DC comprising of at least 12 deluxe tables, 8 medium tables and 24 standard tables. Each factory produces a certain number of tables during each hour it operates. Factory 1 produces 6 deluxe tables and 2 medium tables. Factory 2 produces 2 deluxe tables, 2 medium tables and 12 standard tables. It costs Baltimore Inc. $150 per hour to produce each table in factory 1 and it costs $120 per hour to produce each table from factory 2. The Company wants to determine the number of hours it needs to operate each factory so that it could meet up with its contract at the lowest cost. Hints: You are required to minimize cost assuming that factory 1 = X and factory 2 = Y.

a. Formulate a linear programming model for this problem. (15 points)

b. Represent this problem on a graph using the attached graph paper. Show the feasible region. (10 points)

c. Solve this model by using graphical analysis showing the optimal solution and the rest of the corner points as well as the costs.

The weight of gravel, in kilograms, collected by a power shovel may be modeled by a normal distribution with unknown mean, µ, and standard deviation 50 kg. The weights of a random sample of 20 collections have a mean of 1030 kg. Answer the following questions round all FINAL answers to two decimal places.

(a) What is the point estimate of the mean weight of gravel that the shovel can collect?

(b) Calculate the margin of error for a 95% confidence interval estimate of µ

(c) State the 95% confidence interval for the mean, µ ( , )

(d) What sample size is needed so that the error is no more than 10 kg? n= power shovels

Match the Question with the Test

Researcher's Question: "Does the number of thefts a respondent commits differ significantly based on he respondent's post-release supervision status?" Match the most appropriate statistical test to use for this research question.

Researcher's Question: "Does the number of thefts committed relate significantly to the amount of money per week the respondent makes?" Match the most appropriate statistical test to use for this research question.

Researcher's Question: "Does the number of days a person uses drugs in the past month vary significantly by their living status?" Match the most appropriate statistical test to use for this research question.

Researcher's Question: Does the number of assaults a respondent commits vary significantly based on their level of friends' criminal activity? Match the most appropriate statistical test to use for this research question.

Researcher's Question: Does being re-arrested in the past six months depend significantly on the post-release supervision status? Match the most appropriate statistical test to use for this research question.

A. Chi-Square Test

B. Logistic Regression

C. Analysis of Variance (ANOVA)

D. difference in means test (t-test)

E. Bivariate Correlation (Pearson's r)

In a random sample of 200 adults and 300 teens who watched a certain television show, 50 adults and 150 teens said they liked the show. prove with a 5% significance that the difference between the proportion of adults and adolescents who watch the program is equal to 0.10