If the standard deviation of the mean for the sampling distribution of random samples of size 36 from a large or infinite population is 2, how large must the sample size become if the standard deviation is to be reduced to 1.2? The sample size must become n =
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- In a random sample of 29 residents living in major cities on the West Coast (Group 1) and 29 residents living in major cities on the East Coast (Group 2), each individual was asked their age. The results can be seen in the table below. The population standard deviation of the age in West Coast cities is known to be 11.2 years and in East Coast cities is known to be 9.3 years. Assume the populations are normally distributed. Run a test at a 0.05 level of significance to test if west coast cities are, on average, older. West Coast (Group 1) East Coast (Group 2) 25 34 47 45 18 37 38 20 30 19 50 26 52 79 61 46 40 29 22 55 34 23 35 35 55 36 60 51 68 41 20 50 33 32 36 38 37 26 42 44 60 19 71 28 54 27 20 18 45 30 52 20 34 22 57 43 64 62 Enter the P-Value - round to 4 decimal places. Make sure you put…Suppose x has a distribution with a mean of 13.9 and a standard deviation of 2.1. Random samples of size n=49 are drawn. What would be the mean and standard deviation of the x̄ distribution?Alex wants to find out: if the standard deviation of the mean for the sampling distribution of random samples of size 256 from a large or infinite population is 9, how large must the sample size become if the standard deviation is to be reduced to 2.7 (or even smaller)?
- A leading magazine reported at one time that the average number of weeks an individual is unemployed is 19 weeks. Assume that for the population of all unemployed individuals the length of unemployment is normally distributed where the population mean length of unemployment is 19 weeks and that the population standard deviation is 8 weeks. Suppose you would like to select a random sample of 30 unemployed individuals for a follow-up study.Find the probability that a single randomly selected value is less than 18. P(X < 18) = Find the probability that a sample of size n=30 is randomly selected with a mean less than 18. P(M < 18) = Enter your answers as numbers accurate to 4 decimal places.it is known that the population standard deviation of weight among females is 30. assuming that we have a random sample of 210, what is the standard error of the average weight among women of a sample of this size?A simple random sample of 25 has been collected from a normally distributed population for which it is known the standard deviation is 17. The sample mean has been calculated as 342 and the sample standard deviation of 14.9. Construct a 95% confidential interval for the population mean
- According to the Center for Disease Control and Prevention (CDC), the mean life expectancy in 2015 for Hispanic females was 84.3 years. Assume that the standard deviation was 15 years, as suggested by the Bureau of Economic Research. The distribution of age at death, X, is not normal because it is skewed to the left. Nevertheless, the distribution of the mean, x, in all possible samples of size n is approximately normal if n is large enough, by the central limit theorem. Suppose that Esmé is a researcher for a large, for-profit hospital company. She takes a simple random sample of n = 100 Hispanic females obtained from all death records over the past year. Determine the sample mean, x, such that the probability is 99% that the mean in Esmé's sample will be greater than x. You may find a table of critical values useful. Give your answer to the precise to one decimal place.. x = yearsIn the year 2033, Sarai Patterson is a leading traveling nurse. Sarai is interested in reducing the mean recovery time for patients after experiencing a serious injury (assume recovery times are normally distributed). Suppose the mean recovery time is presently 8.6 months. Sarai takes a random sample of 46 patients that have experienced serious injury to participate in a new treatment program and finds the sample mean is 8.1 months and a sample standard deviation of 1.2 months. Using α = 0.05, answer the following questions. a) What is the setup for your null and alternative hypothesis? b) What is the value of the test statistic? c) What is/are the critical value(s)?A population has a mean of 300 and a standard deviation of 40. Suppose a simple random sample of size 100 is selected and x¯ is used to estimate μ .What is the probability that the sample mean will be within +/- 5 of the population mean?
- Consider the distribution of the average number of hours that college students spend sleeping each weeknight. This distribution is very skewed to the right, with a mean of 5 and a standard deviation of 1. A researcher plans to take a simple random sample of 18 college students. If we were to imagine that we could take all possible random samples of size 18 from the population of college students, the sampling distribution of the average number of hours spent sleeping will have a shape that is ☐ Exactly normal. Just like the population (i.e., very skewed to the right). Less skewed than the population.A random sample of size, nA = 3 is selected from population A, which has a standard deviation of 6. A random sample of size nB = 17 is selected from population B, which has a standard deviation of 12. Is the following statement true or false? The standard error of the mean for the sample from population A is smaller than that for the sample from population B. False True
