Exercise 3 Let assume independent tosses of an unfair six-sided die as 1 1 random experiment with μ = 12'3'3'4'123) Compute likelihood of observing D = 2,4,5,1,3.
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- Question 3 For each question, enter T for true or F for false. • 1. The purpose of Randomized Block Design ANOVA is to check if the alternative hypothesis is true. • 2. Three assumptions are required to justify using Randomized Block Design ANOVA. They are: A. the sample in each cell is selected randomly from a normal population, B. the variances in the treatment groups are equal, C. there is no interaction between blocks and treatments. • 3. For Randomized Block Design ANOVA, ignoring subscripts, the linear model is x=u+B+T+e • 4. In the equation in #3 above, B is the blocking effect and u is the sample average.The number of people likely to get infection due to COVID19 during the month of April 2021 is an example of Interva Ratio Nominal Ordinal random variable continuous random variableFor this part of the project, you will investigate one question about a first-year nursingthe class who attends GetAnOnlineNursingDegreeFromSouthernNebraskalnstituteUniversity.comregarding weight changes during their first year of college. 4. At the 0.05 level, can we conclude there is a difference between the students’ fallweight and spring weight?random numbers from april 22.02, 20.15, 18.93, 19.78, 24.74, 26.72, 20.23, 40.86, 19.83,20.9 23.6, 22.4,18.89, 20.26, 19.48, 25.88, 20.96, 30.26, 28.17, 19.7 Determine whether your sample provides statistical evidence of a difference between the students’ fall weight (before) and spring weight (after). Set alpha at 0.05. (Yes, hypothesis testing...butwhich one?
- True or False: Let X be the number of 3's in 8 rolls of a 6-faced fair die. X can be approximated as a Poisson random variable.(with explanations)Two new machines for producing tires have been proposed by a worker in a manufacture. The manufacture believes there will be no difference in the strength of tires produced by these machines. To test this hypothesis, a sample of 9 tires produced by machine 1 and 7 tires produced by machine 2 were randomly selected. It is known from previous experience that the strength of a tire produced using machine 1 is a normal random variable with standard deviation equals to 3. And the strength of a tire produced using machine 2 is also a normal random variable with standard deviation equals to 4. use the following information to answer the following questions: Machine 1Machine 2 6.5 1.0 6.7 2.5 5.8 3.2 4.9 3.1 5.3 4.5 4.0 5.7 3.1 1.5 5.7 4.3 i. Find the estimated difference mean strength of tires produced using both machines [ X1-X2] . O0.06 ONone of these O-2.18 O2.07 O-0.25The FDA regulates that a fish that is consumed is allowed to contain at most 1 mg/kg of mercury. In Florida, bass fish were collected in 59 different lakes to measure the amount of mercury in the fish from each of the 59 lakes. Do the data provide enough evidence to show that the fish in all Florida lakes have a mercury level higher than the allowable amount? State the random variable, population parameter, and hypotheses.a) The symbol for the random variable involved in this problem is The wording for the random variable in context is as follows: b) The symbol for the parameter involved in this problem is The wording for the parameter in context is as follows: c) Fill in the correct null and alternative hypotheses: H0:H0: HA:HA: d) A Type I error in the context of this problem would be: e) A Type II error in the context of this problem would be:
- An analysis of personal loans at a local bank revealed the following facts: 10% of all personal loans are in default (D), 90% of all personal loans are not in default (D'), 20% of those in default are homeowners (HID), and 70% of those not in default are homeowners (H | D'). If a personal loan is selected at random P (H _n D') = _____. 0.63 0.78 O 0.20 0.18 0.90Assume that a simple random sample has been selected from a normally distributed population. Identify the null hypothesis, alternative hypothesis, test statistic, P-value (or range of p-values), conclusion about the null hypothesis, and final conclusion that addresses the original claim. 1) Test the claim that the mean age of the graduate school population in one city is less than 33 years. Sample data are summarized as n 67, x = 42.4 years, and s = 31.5 years. Use a significance level of a = 0.10.b) Suppose that Y₁, Y₂,..., Y₁0 is a random sample from a bernoulli (P) distribution. It is desired that the null hypothesis Ho: P = 0.5 against the alternative hypothesis H₁: P = 0.1 at a level of significance. If Ho is rejected when Σı Y = 1. i) Determine the level of significance. ii) Find the power of the test.
- In a certain vaccination site, the service time for individuals before they were given a vaccine shot is modeled as a random variable X with mean µ = 90 seconds and variance o? = 9 minutes?. Assuming that the service times for each individual are independent and identically distributed, determine the probability of vaccinating 400 individuals within 9 hours.3) A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor's bank checks the waiting times at both banks. Assume the samples are random and independent, and the populations are normally distributed. Test the local bank's claim assuming that o*o5. Use a = 0.02. Use the P-value approach. Local Bank Competitor Bank n1 = 36 n2 = 42 X1 = 5.1 minutes s1 = 1.1 minutes X2 = 5.6 minutes s2 = 1.0 minutesTwo new machines for producing tires have been proposed by a worker in a manufacture. The manufacture believes there will be no difference in the strength of tires produced by these machines. To test this hypothesis, a sample of 9 tires produced by machine 1 and 7 tires produced by machine 2 were randomly selected. It is known from previous experience that the strength of a tire produced using machine 1 is a normal random variable with standard deviation equals to 3. And the strength of a tire produced using machine 2 is also a normal random variable with standard deviation equals to 4. use the following information to answer the following questions: 1. Find the estimated difference mean strength of tires produced using both machines [X-X) 2. What is the value of the test statistic : ii. If p-value was found equal to 0.12, What is the appropriate conclusion?