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- 2.2. Let Y₁, Y₂Yn denote a random sample from a gamma distribution with each Y-gamma (0; B) with known. Find a sufficient statistic for 8.3. Let X N(u,0²). Find the MSE of the (uncorrected) sample variance 152 as an estimator for ² and compare with the MSE of the (corrected) sample variance S².suppose that 43% of people who enter a store will make a purchase. Random samples of people who walk into a particular store is studied, and the proportion of those who made a purchase is found for each sample. Assume that all the samples were the same size. If 29.46% of all sample proportions are less than 0.3274. What was the z-score for 0.3274? What is σp′?
- 14) The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is 11.0. As a member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight full-time faculty for one week is shown in the table below. At α=0.01, can you reject the dean's claim? Complete parts (a) through (d) below. Assume the population is normally distributed. 12.27.711.57.16.19.514.69.9 (a) Write the claim mathematically and identify H0 and Ha. Which of the following correctly states H0 and Ha? A. H0: μ>11.0 Ha: μ≤11.0 B. H0: μ<11.0 Ha: μ≥11.0 C. H0: μ≤11.0 Ha: μ>11.0 D. H0: μ=11.0 Ha: μ≠11.0 E. H0: μ≥11.0 Ha: μ<11.0 F. H0: μ≠11.0 Ha: F. H0: μ≠11.0 Ha: μ=11.0 (b) Use technology to find the P-value. P= (Round to three decimal places as needed.) (c) Decide whether to reject or fail to reject the null…1. A sample of n=16 observations is drawn from a normal population with u = 1000 and o = 200. Find the following: a P(X>1050) b P(X1100) =14.44 (EX) Cicadas as fertilizer? Every 17 years, swarms of cicadas emerge from the ground in the eastern United States, live for about six weeks, and then die. There are so many cicadas that their dead bodies can serve as fertilizer. In an experiment, a researcher added cicadas under some plants in a natural plot of bellflowers on the forest floor, leaving other plants undisturbed. In this experiment, cicada-supplemented bellflowers from a natural field population produced foliage with 12% greater nitrogen content relative to controls (P = 0.031). A colleague who knows no statistics says that an increase of 12% isn't a lot - maybe it's just an accident due to natural variation among the plants. Explain in simple language how P = 0.031 answers this objection. O The maximum difference in nitrogen content between cicada-supplemented bellflowers and controls is 0.031. This small value is good evidence that the null Hypothesis is true. O Assuming no difference in nitrogen content, the…
- 2. Suppose it is claimed that amongst the population of STM1001 students, the number of items bought online in the past year is normally distributed with a mean of μ = 20 and variance of o² = 25. Further suppose that we wish to study the mean of the population by taking a random sample of n = 61 STM1001 students. Using this information, write down the distribution of the sample mean YN 3. Following on from the previous question, what is the probability tha when we take a random sample of n 61 STM1001 students, the sample mean would be greater than 20.3521? 5. A What known thatSuppose that the makers of Duracell batteries want to demonstrate that their size AAbattery lasts an average of at least 45 minutes longer than Duracell’s main competitor,the Energizer. Two independent random samples of 100 batteries of each kind areselected, and the batteries are run continuously until they are no longer operational. Thesample average life for Duracell is found to be 308 minutes. The result for the Energizerbatteries is 254 minutes. Assume the entire AA batteries standard deviation 84 minutesand Duracell batteries 67 minutes. Is there evidence to substantiate Duracell’s claim thatits batteries last, on average, at least 45 minutes longer than Energizer batteries of thesame size? (assuming equal population variances)7. Let Xi denote a binary variable, and consider the regression Yi = β0 + β1Xi + ui. Let Y ̄0 denote the sample mean for observations with X = 0, and Y ̄1 denote the sample mean for observations with X = 1. Show that βˆ0 = Y ̄0, βˆ0 + βˆ1 = Y ̄1, and βˆ1 = Y ̄1 − Y ̄0.
- Suppose a simple random sample of size n = 125 is obtained from a population whose size is N = 30,000 and whose population proportion with a specified characteristic is p = 0.68.4. 3. In a survey of 480 drivers from the South, 392 wear a seat belt. In a survey of 340 drivers from the Northeast, 293 wear a seat belt. At α=0.07, can you support the claim that the proportion of drivers who wear seat belts is greater in the South than in the Northeast? Assume the random samples are independent. Complete parts (a) through (e). (a) Identify the claim and state H0 and Ha. The claim is "the proportion of drivers who wear seat belts in the South is (1) in the Northeast." Let p1 represent the population proportion for the South, and p2 represent the population proportion for the Northeast. State H0 and Ha. Choose the correct answer below. A. H0: p1=p2 Ha: p1≠p2 B. H0: p1>p2 Ha: p1≤p2 C. H0: p1<p2 Ha: p1≥p2 D. H0: p1≠p2 Ha: p1=p2 E. H0: p1≥p2 Ha: p1<p2 F. H0: p1≤p2 Ha: p1>p2 (b) Find the critical value(s) and identify the rejection region(s).…Suppose our population is made up of the 12 individuals whose monthly INCOME: 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 Solve for (MU) and (SIGMA) for the variable income. Do not convert to thousands to simplify our calculations. Do not round off the parameters. If our sample size is 2, how many unique samples can be derived from this population?