Suppose a random sample of 900 measurements is taken from an unknown population. The average of these measurements is an approximate normal random variable with a mean that is
equal to the mean of the population.
equal to the standard deviation divided by 30.
equal to the population mean divided by 900.
always less than the population mean.
equal to the population mean divided by 30.
According to the central limit theorem, if we draw large sample (n>30) from population with mean and variance , then the sampling distribution of sample mean is approximately normally distributed with mean and variance .
Therefore, the average of these measurements is an approximate
normal random variable with a mean that is "equal to the
mean of the population
."
Answer is (a)
Suppose a random sample of 900 measurements is taken from an unknown population. The average of...
Suppose that a random sample of size 1 is to be taken from a finite population of size N. Answer parts (a) through (c) below. a. How many possible samples are there? A. N + 1 B. N-1 0 C. N D. 1 b. Identify the relationship between the possible sample means and the possible observations of the variable under consideration. Choose the correct answer below. A. Each possible sample mean is equal to an observation, only if the population...
Suppose a random sample of 49 measurements is selected from a population with a mean of 44 and a standard deviation of 1.1. What is the mean and standard error of X?
A random sample of 49 measurements from one population had a sample mean of 18, with sample standard deviation 5. An independent random sample of 64 measurements from a second population had a sample mean of 21, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01. (a) What distribution does the sample test statistic follow? Explain. The standard normal. We assume that both population distributions are approximately normal with unknown...
and for 2. A random sample of n measurements is selected from a population with unknown mean known standard deviation o = 10. Calculate the width of a 95% confidence interval for these values of n: a. n=100 b. n=200 c. n=400 d. n=1000 e. n=2000
Suppose that a simple random sample is taken from a normal population having a standard deviation of 15 for the purpose of obtaining a 95% confidence interval for the mean of the population. a. If the sample size is 44, obtain the margin of error. b. Repeat part (a) for a sample size of 25
Suppose a random sample of n = 87 measurements is selected from a population with mean μ = 24 and standard deviation σ = 8. Find the value of the standard error, (round to 1 decimal place). = ?
A random sample of size 36 is to be taken from a population that is normally distributed with mean 60 and standard deviation 18. The sample mean of the observations in our sample is to be computed. The sampling distribution of the sample mean is Select one: . a. normal with mean 36 and standard deviation 18. O b. normal with mean 60 and standard deviation 0.5. c. normal with mean 60 and standard deviation 3. d. normal with mean...
Suppose that a simple random sample is taken from a normal population having a standard deviation of 6 for the purpose of obtaining a 90% confidence interval for the mean of the population. The margin of error for a sample size of 16 is ??? (Round to four decimal places as needed.) The margin of error for a sample size of 81 is ??? (Round to four decimal places as needed.)
Suppose that a random sample of size 64 is to be selected from a population with mean 30 and standard deviation 7. (Use a table or technology.) (a) What are the mean and standard deviation of the sampling distribution of x? - 30 0 - 0.875 Describe the shape of the sampling distribution of x. The shape of the sampling distribution of x is approximately normale (b) What is the approximate probability that x will be within 0.5 of the...
A random sample of n measurements was selected from a population with unknown mean μ and standard deviation σ = 35 for each of the situations in parts a through d. Calculate a 99% confidence interval for μ for each of these situations. a. n = 75, x = 20 Interval: ( _____, _____ ) b. n = 150, x = 104 Interval: ( _____, _____ ) c. n = 90, x = 16 Interval: ( _____, _____ ) d....