Example 4: Thirty-five successive samples of 100 castings each, taken from a production line, contained respectively, 3, 3, 5, 3, 5, 0, 3, 2, 3, 5, 6, 5, 9, 1, 2. 4, 5, 2, 0, 10, 3, 6, 3, 2, 5, 6, 3, 3, 2, 5, 1, 0, 7, 4 and 3 defectives. If the fraction defective is to be maintained at 0.02, construct a p-chart for these data.
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- A population consists of the following 6 values: {10, 20, 30, 40, 50, 60}. A sample of size 3 will be chosen from this population without replacement and the median of the sample will be computed: { (0.5 (£n/2 + £n/2+1) m = x(n+1)/2 n odd n even In other words, in a sample of size n = 3 ordered from smallest to largest the median is the 2nd number. The median of a discrete random variable, μ, is defined as the value of such that and P(X M) ≤ 0.5 Determine the median of the population. Think of the population as an equally likely sample space. Determine the sampling distribution of the sample median, m for this population by (1) identifying all possible samples (how many are there?), (2) calculating the median in each sample and (3) using that to determine the probability of each median. Calculate E (m) Determine the standard error or the sample medianFor each of these 10 samples, compute Statistics 1, 2, and 3. Enter your answers as 3 numbers separated by commas, such as 1,2,3. 2, 3, 3* 2, 3, 4 2, 3, 4* 2, 3*, 4 2, 3*,4* 2, 4, 4* 3, 3*, 4 3, 3*, 4* 3, 4, 4* 3*, 4, 4* Which statistic would you recommend for estimating u? Average of smallest and largest values in the sample Question Heln5-The number of contaminating particles on a silicon wafer prior to a certain rinsing process was determined for each wafer in a sample size 100, resulting in the following frequencies: Cumulative Frequency 1 TITI Cumulative Number of Particles Number of Particles Frequency 84 1 3 88 2 6 10 93 3 18 11 96 4 29 12 97 5 44 13 99 6 62 14 100 7 72 a) What proportion of the sampled wafers had (P2 8)? b) What proportion of the sampled wafers had between (5 < P < 10)?
- 1. XYZ Cable corporation employs 2,500 people. If a random sample of 165 is taken from the entire population by systematic sampling. From which number will you choose the starting number?1. Explain the difference between z-tests (which use categorical data), and t-tests (which use numerical data). 2. Conduct a t-test, both when given statistics, and when given data. 3. Conduct a t-test, 2-sample t-test, and paired t-test. 4. Differentiate between the five types of tests we have learned so far.26) A phycologist is interested in determining the proportion of algae samples from a local rivulet that belonged to a particular phylum. A random sample of 50 algae was obtained and each alga was categorized as either being cyanobacteria or not. It was found that 38 were, in fact, cyanobacteria. a) The proportion p that was cyanobacteria isA. 38B. 0.38C. 0.5D. 0.76E. 50 b) (Continue from the previous question),What is the standard error of the proportion p, i.e. S.E.(p), that were cyanobacteriaisA. 0.0036B. 0.0604C. 0.0684D. 0.1824E. None of the above
- Consider the following population of ten digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. a. Find 3 random samples of the five digits from the list. Record the elements of each sample. b. find the arithmetic average of each sample. (Hint: to find the average, sum the data enteries and divide the sum by the number of enteries in the sample.) there is a line over each of these x1 = x2= x3= c. comment on how your results compare with the average of the entire population.Description 13. A lot of 400 items that actually contains 3 defective items is subject to the following double sampling plan: the lot is accepted if a first sample of 5 contains no defectives; the lot is rejected if this sample contains 2 or more defectives; if the first sample contains 1 defective, a second sample of 7 is drawn; the lot is accepted if the second sample contains no more than 1 defective, otherwise the lot is rejected. Suppose that at any stage an unacceptable item is replaced by a good item. (a) What is the probability the lot is accepted? (b) What is the AOQ if all the defective items in unacceptable lots are replaced by good items? (c) Show the OC curve for the sampling planA population consists of a batch of 24,683 aspirin tablets, and it includes 1,050 that are defective because they do not meet specifications. A random sample of n = 200 of the tablets is obtained and tested, with the result that 15 of them are defective. a. What is the population proportion, p, of defective aspirin tablets? b. What is the sample proportion, p, of defective tablets? c. How can the discrepancy between the population proportion and the sample proportion be explained? a. The population proportion of defective aspirin tablets is p = (Round to three decimal places as needed.) b. The sample proportion of defective aspirin tablets is p= (Round to three decimal places as needed.) c. Choose the correct answer below. C O A. There will always be a discrepancy between the population proportion and the sample proportion when the sample size is small. O B. Random samples collected with sound sampling methods vary, and the sample proportions differ from the population proportion…
- 1. A lawn mower company will produce 1,500 lawn mowers by 2020. In an effort to determine how much maintenance free consumers will take when they already buy lawn mowers, the company decided to conduct a study over the past 1 year of these mowers. . First, a random sample was taken by contacting 200 grass mowers. The company owner provides an 800 number and is asked to contact the company when the first repair is needed for the lawn mower. Owners who no longer use lawn mowers to cut their grass are either disqualified or not sampled. After 1 year, it turned out that 187 owners had reported for the first repair. However, the other 50 disqualified themselves. The average number per year until the first improvement was 5.3 times for samples deemed feasible. It is believed that the standard deviation is 1.28 per year. If the company wants to advertise the lawnmower and with a confidence level of 95%, what is the estimated annual mean value of repair-free lawn mower for this lawn mower?…1. Suppose there are nine sections of Intro Stats with 25 students each. You ‘randomly’ choose two studentsfrom each section to use as asample. Which of the following results best describes this type of sample?A. a random, stratified sampleB. a simple random sampleC. a random, clustered sampleD. a non-random, systematic sampleE. a random, convenient sample 2. Suppose there are nine sections of Intro Stats with 25 students each. You place all 225 student’s namesin a hat and ‘randomly’ draw 30 student names to use as asample. Which of the following results bestdescribes this type of sample?A. a random, stratified sampleB. a simple random sampleC. a random, clustered sampleD. a non-random, systematic sampleE. a random, convenient sample 3. Assume the heights of students at College are normally distributed with a mean of 64.0 inchesand a standard deviation of 1.2 inches. Which of the following values best approximates the probabilityof randomly selecting aCollege student tallerthan 62.2…1. The incidence of cancer among phosphate mine workers and their exposure to radiation was investigated. Cancer incidence was recorded among 60 phosphate mine workers who had 0-29 working level months (WLM) of exposure, 60 phosphate mine workers who had 30-89 WLM of exposure, and 60 phosphate mine workers who had 90-120 WLM of exposure. The number of cancer incidences for each group are presented in Table 1. Table 1: Two-way Table of Counts Cancer Incidence Exposure Level Yes No Total 0-29 WLM 20 40 60 30-89 WLM 33 27 60 90-120 WLM 43 17 60 Total 96 84 180 Perform a x? test, at the 5% level of significance, whether cancer incidence rates differ between the three levels of radiation among phosphate mine workers.