8.18 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?
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- 1. A population is normally distributed with a mean of-30 (negative 30) and a standard deviation of 4. (Show work) a. What is the mean of the sampling distribution (HM) for this population? b. If a sample of 16 participants is selected from the population, what is the standard error of the mean?6.1 Suppose a normal distribution has a mean of 5 and a standard deviation of 1.8. What is the z-score of x = 8.9? Round to 1 decimal place.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?
- 4. A distribution of scores has = 70. The z-score for X = 65 is computed and a value of z = +1.00. Regardless of the value of the standard deviation, why must this z-score be incorrect?8. In a population with a standard deviation of o = 5, a score of X = 44 corresponds to a z-score of z= 2.00. What is the population mean?4. A normal population has the mean of 20 and the variance of 100. A random sample of size n = 69 is selected. (a) Find the standard deviation of the sample mean. (b) How large must the sample be if you want to halve the standard deviation of the sample mean?
- 5. The variance on 17 bags of apples is found to be 5.5. The company that bags the apples claims that the standard deviation of its apples is 2. Test their claim. Use a = 0.05The ages of a group of 149 randomly selected adult females have a standard deviation of 16.5 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=16.5 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statisticsstudents? Assume that we want 90% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population? Question content area bottom Part 1 The required sample size is enter your response here.The ages of a group of 156 randomly selected adult females have a standard deviation of 17.4 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=17.4 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 98% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?
- 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.5. The distribution of heights of a certain breed of terrier has a mean of 72 centimeters and a standard deviation of 10 centimeters, whereas the distribution of heights of a certain breed of poodle has a mcan of 28 centimeters with a standard deviation of 5 centimcters. Assume the distributions of both types of breeds are normally distributed. (n) Suppose we are taking a random sample of 64 terriers. What is the sampling distri- bution of mean heights of the breed of terriers? (b) Find the probability that the sample mean for a random sample of heights of 61 terriers excoedls 75 centimetcrs. (c) Find the probability that the sample mean for a random sample of heights of 64 terriers excoeds the sample mean for a random sample of heights of 100 poodles by at lenst 44.2 centimeters.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