A study showed that 70% of the people shop online. In 2013 a random sample of 1500. In 2014 a random sample of 1000. 1. Calculate 99% CI 2. What's the minimum sample size, with error of 0.10 for 95% CI
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- A medical researcher says that less than 80% of adults in a certain country think that healthy children should be required to be vaccinated. In a random sample of 200 adults in that country, 76% think that healthy children should be required to be vaccinated. At α=0.05, is there enough evidence to support the researcher's claim? Complete parts (a) through (e) below. Let p be the population proportion of successes, where a success is an adult in the country who thinks that healthy children should be required to be vaccinated. (a) Find the critical value(s) and identify the rejection region(s). z0=______ (b) Identify the rejection region(s). (c) Find the standardized test statistic z. z=______ (d) Decide whether to reject or fail to reject the null hypothesis and (e) interpret the decision in the context of the original claim.Dr. Castillejo feels that the maximum pulse rate during the run is a good predictor in explaining the oxygen consumption in the blood stream. He asserts that if the pulse rate at the end of the run increased, then the oxygen consumption will also increase, hence his/her heart is functioning well. Based on the R commanderoutput below, check if the data on oxygen consumption and maximum pulse rate (from 152 bpm to 196bpm) support Dr. Castillejo’s assertion.To study the effect of alloying on the resistance of electric wires, an engineer plans to measure the resis-tance of n1 = 35 standard wires and n2 = 45 alloyed wires. If it can be assumed that σ1 = 0.004 ohm andσ2 = 0.005 ohm for such data, what can she assert with98% confidence about the maximum error if she usesx1 − x2 as an estimate of μ1 − μ2? (Hint: Use the result ofExercise 8.)
- Find the maximum likelihood estimator by getting the derivative and equating it to 0A company specializing in building robots that clean your house has found that the average amount of time kids spend cleaning their houses is about 2 hours per week with a margin error of 15 minutes. Which of the following is the correct window of time t (in minutes) we can expect the population of kids to take cleaning their rooms?A research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that they would travel into space on a commercial flight if they could afford it. At α=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. Identify the P-value?
- what is the conventional minimum power a study should have? For a study with this minimum power, what is tthe probablility that you will fail to reject the null hypothesis if the research hypothesis is true?In a café, the manager wishes to estimate p, the proportion of customers who will order sandwich for their lunch. Suppose 30 out of 300 customers will order sandwich for their lunch. Find the probability that more than 40 customers will order sandwich for their lunch by using a suitable approximationA sample has a minimum value of 7 and a maximum value of 58 .Estimate its variance.
- The germination rate of seeds is defined as the proportion of seeds that, when properly planted and watered, sprout and grow. A certain variety of grass seed usually has a germination rate of 0.80, and a company wants to see if spraying the seeds with a chemical that is known to change germination rates in other species will change the germination rate of this grass species. (a) Suppose the company plans to spray a random sample of 400 seeds and conduct a two-sided test of 0: 0.8Hpusing = 0.05. They determine that the power of this test against the alternative 0.75pis 0.69. Interpret the power of this test.(b) Describe two ways the company can increase the power of the test. What is a disadvantage of each of these ways? (c) The company researchers spray 400 seeds with the chemical and 307 of the seeds germinate. This produces a 95% confidence interval for the proportion of seeds that germinate of (0.726, 0.809). Use this confidence interval to determine whether the test described in…A sample of 200 bolts from one machine showed that 15 were defective, while a sample of 100 bolts from another machine showed that 12 were defective. Find the (a) 95%, (b)99.73% confidence limits for the difference in proportions of defective bolts from the two machines. Discuss the results obtained.Let X1, ..., Xn be a sample from an exponential population with parameter λ.(a) Find the maximum likelihood estimator for λ. (b) Is the estimator unbiased?(c) Is the estimator consistent?