(a) Define the sampling frame and elementary unit.
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- 2. City officials are interested in identifying the most dangerous intersections in State College. The city records the number of car accidents at each of n intersections over the course of the year. Let's assume that the number of accidents for a particular intersection i is denoted by X₁. We are provided with a simple random sample of accidents at n intersections, X₁,..., Xn. Let's assume the following model, i.i.d. Xi Pois (X) where A is an unknown parameter of interest (i.e., the unknown population accident rate). (a) the sufficient statistic? Show that the MLE of λ is X. Find its sufficient statistic. Is the MLE a function of Find the bias, variance, and MSE of ÂMLE. Does the MLE achieve the Cramér-Rao's lower bound? (b) (c) (d) Find the asymptotic distribution of the MLE for A. (e) Now, the officials are interested in the total number of accidents expected in those n intersections, that is, E(X1 X₂) = nλ. Let us denote this expected total as (= nλ). Find the MLE of 0. (Hint:…0:00 Time Tak-nd):26:40 Question 4 (1 point) Toronto was divided to 80 geographical areas and all the residents in 8 geographical areas, chosen at random, were surveyed. This is an example of 2. Simple Random Sampling Sade Darajat Attempt 1 b. Stratified Random Sampling C. Systematic Random Sampling Od. Cluster Random Sampling Question 5 (1 point) A sample of 18 students were asked how many courses they passed last year. The variable in this question and its corresponding measurement scale are as follows: a. Discrete, Ordinal b. Qualitative, Nominal O c. Quantitative Continuous, Nominal d. Quantitative Discrete, Interval Question 6 (1 point) 1. A random sample of 93 students were surveyed at a school. If this sample represents 6% of the population. what is the school population? Ⓒa. 1550 b. 1870 Ⓒc. 1700 Ⓒd. 1800Include a diagram of the distribution indicating important components of the question
- Types of Random Sampling Give the appropriate type of random sampling for each item. Justify your answers. A researcher from SWS survey picked the cities of Las Piñas, Pateros, Pasig, and San Juan, out of 17 cities of NCR, to be the part of a nationwide survey. The whole populace of the said cities will be interviewed to determine the government response satisfaction rate for COVID-19 crisis. A survey is being conducted to determine if the students are satisfied to the foods that are being served in their school canteen. School administrators picked 20% of the respondents from Grade 7, 30% from Grade 8, 35% from Grade 9, and 15% from Grade 10. A researcher chose the subjects of their study by selecting every 11th member of the population.A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 6. 7 8. 9 10 11 12 Brand 1 0.38 0.51 0.40 0.32 0.43 0.62 0.32 0.40 0.64 0.38 0.64 0.46 Brand 2 0.28 0.52 0.32 0.28 0.41 0.61 0.44 0.33 0.50 0.34 0.52 0.48 Difference 0.10 -0.01 0.08 0.04 0.02 0.01 -0.12 0.07 0.14 0.04 0.12 -0.02 (Brand 1 - Brand 2) Send data to calculator Based on these data, can the consumer group conclude, at the 0.01 level of significance,…A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in Table 1. Car Brand 1 Brand 2 Difference(Brand 1 - Brand 2) 1 0.362 0.235 0.127 2 0.343 0.368 -0.025 3 0.203 0.230 -0.027 4 0.335 0.247 0.088 5 0.207 0.221 -0.014 6 0.344 0.332 0.012 7 0.354 0.285 0.069 8 0.385 0.382 0.003 9 0.273 0.236 0.037 10 0.376 0.328 0.048 Table 1 Based on these data, can the consumer group conclude, at the 0.05 level of…
- A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 10 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Based on these data, can the consumer group conclude, at the 0.01 level of significance, that the mean tread wears of the brands differ? Answer this question by performing a hypothesis test regarding μd (which is μ with a letter "d" subscript), the population mean difference in tread wear for the two brands of tires. Assume that this population of differences (Brand 1…A B CThe Federal Reserve has called remote deposit capture (RDC) "the most important development the [U.S] banking industury has seen in years." This service allows users to scan checks and to transmit the scanned images to the bank for posting. In its annual survey of community banks, the American Bankers Association asked banks whether or not they offered this service. The two way table is given for this exercise in figure 9.9. Use the figure to find the joint distribution, the two marginal distributions, and the conditional distributions. Which conditional distribution would you use to explain the results of your analysis? Give a reason for your preference.
- A consumer products testing group is evaluating two competing brands of tires, Brand 1 and Brand 2. Tread wear can vary considerably depending on the type of car, and the group is trying to eliminate this effect by installing the two brands on the same random sample of 12 cars. In particular, each car has one tire of each brand on its front wheels, with half of the cars chosen at random to have Brand 1 on the left front wheel, and the rest to have Brand 2 there. After all of the cars are driven over the standard test course for 20,000 miles, the amount of tread wear (in inches) is recorded, as shown in the table below. Car 1 2 3 4 5 6 7 8 9 10 11 12 Brand 1 0.35 0.37 0.51 0.59 0.59 0.42 0.59 0.35 0.38 0.40 0.51 0.34 Brand 2 0.37 0.41 0.49 0.48 0.41 0.21 0.53 0.34 0.34 0.48 0.26 0.19 Difference(Brand 1 - Brand 2) −0.02 −0.04…1-If testing the difference between two population proportions under independent sampling, you pool the sample proportions and compute as p=(x1+x2/ (n1+n2). Group of answer choices if the population proportions are assumed equal if the difference in the population proportions is hypothesized to be different than zero All of these choices are correct if the difference in the population proportions is hypothesized to be zero. 2-A consumer magazine wants to figure out which of two major airlines lost a higher proportion of luggage on international flights. The magazine surveyed Standard Air (population 1) and Down Under airlines (population 2). Standard Air lost 45 out of 600 bags. Down Under airlines lost 25 of 450 bags. Does Standard Air have a higher population proportion of lost bags on international flights? Which of the following is the appropriate p-value? Group of answer choices 0.1056 0.1634 0.0817 0.8366 Please step by step answer.SHOW WORK TO GET FULL CREDIT Problem 3) This problem has two independent parts a) and b) a) (6 points) A gasoline tank for a certain vehicle is designed to hold 16 gallons of gas. Suppose that the actual capacity of a randomly selected tank has a distribution that is approximately Normal with a mean of 16.0 gallons and a variance of 0.0256 gallons?. The manufacturer of this gasoline tank considers the largest 2% of these tanks too large to put on the market. How large does a tank have to be to be considered too large? (Round your answer to 2 decimal places) (Show work). b) (4 points) The number of telephone calls that arrive at a phone exchange is a random variable that follows a Poisson distribution. The expected number of calls per hour at the exchange is 4. What is the mean time between consecutive telephone calls? (Show work)
