sample size of 3 is taken from
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Suppose that a population consists of only 5 members and the values of are as follows.
| Member | 1 | 2 | 3 | 4 | 5 |
| Y | 5 | 3 | 5 | 2 | 2 |
a) If a
b) Enumerate all possible outcomes of a random sampling of size 3 (in a table). For each outcome, compute for the sample mean ( and sample variance. No need to show solution in this part
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- Twenty different statistic students are randomly selected. For each of them,their body temperature (° F) is measured and their head circumference (in) ismeasured. Without doing any research or calculations, estimate the value of r. Forthis sample of paired data, what does r represent?2. In a population it is estimated that 20% have a desired trait of interest for the researcher. The researcher wants to know how many people on average he has to draw from a population to get 2 people with the trait. Use rows 20-24 of the Random Number Table to carry out the simulation. Explain clearly how you set up the problem and report your findings. Answer:If samples of a fixed size N are drawn randomly and with replacement from the same population of scores, should we expect the sample means to differ across samples? why or why not?
- missing entires in a probability density function. Use the following density function instead of the one in your text. Value of X Probability Product -2 (A) -0.4 |--1 (B) -0.3 (C) 0.3 0.3 2 0.2 (D) (1) What is the value of (A)? -2 (2) What is the value of (B)? (3) What is the value of (C)? (4) What is the value of (D)?A researcher wishes to select a stratified random sample from a population with 3 strata as follows (with the usual notation): Н Nh Sn Ch 1 300 30 25 500 40 49 3 200 20 36 If the budget is $5000 and the overheads $800, find the allocations for each stratum and estimate the variance of sample meanusing the allocation method. By using proportional allocation, estimate the variance and compare it to the variance from part (1). Determine the total cost from the allocation of part (2). Explain your result. (1) (2) (3)A population consists of the two numbers (7, 8). Consider all possible samples ofsize 2 that can be drawn with replacement from this population. Find the following:a. The mean of the sampling distribution of meansb. The variance of the sampling distributionc. The standard deviation of the sampling distribution of means.d. Illustrate the probability histogram of the sampling distribution of themeans. The average number of liters of water that a person consumes in a month is 12 liters. Assume that the standard deviation is 4.5 liters and the distribution isapproximately normal.a. Find the probability that a person selected at random consumes morethan 13 liters per month.b. If a sample of 20 individuals is selected, find the probability that mean ofthe sample will be more than 13 liters. Identify the region under the t-distribution corresponding to the t-value which is 1.440 and the area is on both sides of the t-distribution. Identify the region under the t-distribution corresponding to…
- A statistics teacher asked two different students, Lexie and Jennifer, to go to Wegmans and sample 30 shoppers each. The population of interest for both people can be defined as, “People who shop at the Johnson City, NY Wegmans store”. Here is what each person did to collect their sample: Lexie: She stood outside at the entrance to the store on 3 different days and times and surveyed every 15th person to walk by her. She surveyed 10 people each time to get her 30. Jennifer: She went to Wegmans after her nursing shift first thing Wednesday morning to buy deodorant since she ran out. When she was in the pharmacy area she surveyed all the people around her and then, to get up to 30 surveys, she went to the health food section and surveyed everyone she was there. Identify at least 2 specific reasons why Lexie’s approach is more likely to give a representative sample. Consider sources of bias, or types of shoppers who might be excluded by Jennifer’s approach.…Suppose that we have disjoint normal populations A and B with equal but unknown population variances. Suppose we plan a sample of size 12 from from population A and a sample of size 6 from population B which we will pool to form the pooled variance. If the sample variance for the sample from population A is 25 and the sample variance for the sample from population B is 36, then what is the pooled sample variance?The single sample z test may be used to determine: a)the variability in the sample b)if a sample mean is different from a known population mean c)if two population means are different d)the variability in the population of sample means
