We draw a random sample of size 49 from a normal population with variance 2.1. If...

We draw a random sample of size 49 from a normal population with variance 2.1. If the sample mean is 21.5, what is a 99% confidence interval for the population mean?

Solutions

Expert Solution

Solution :

Given that,

Sample size = n = 49

Z/2 = 2.576

Margin of error = E = Z/2* ( / $\sqrt$ n)

= 2.576 * (1.4491 / $\sqrt$ 49)

Margin of error = E = 0.5

At 99% confidence interval estimate of the population mean is,

- E < < + E

21.5 - 0.5 < < 21.5 + 0.5

21 < < 22

(21 , 22)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Random sample of size 7 is drawn from a normal population with variance 2.5 the sample...

Random sample of size 7 is drawn from a normal population with variance 2.5 the sample observations are 9, 16, 10, 14, 8, 13, 14. find 99% confidence interval for the population mean what would be the confidence interval if the variance is unknown.

We draw a random sample of size 36 from a population with standard deviation 3.2. If...

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean? [26.7550, 28.2450] [25.9547, 28.0453] [25.8567, 28.1433] [26.8401, 27.1599]

We draw a random sample of size 36 from a population with standard deviation 3.2. If...

We draw a random sample of size 36 from a population with standard deviation 3.2. If the sample mean is 27, what is a 95% confidence interval for the population mean?

Say that a sample of size 49 taken from a normally distributed population, has variance =...

Say that a sample of size 49 taken from a normally distributed population, has variance = 1. The sample has a mean of 0.49. Then, a 95% confidence interval for µ will be 0.49 – (1.96)(1/7) < µ < 0.49 + (1.96)(1/7) 0.49 – (2.575)(1/7) < µ < 0.49 + (1.96)(1/7) 49 – (1.96)(1/0.7) < µ < 49 + (1.96)(1/0.7) 49 – (2.575)(1/0.7) < µ < 49 + (2.575)(1/0.7)

4 We draw a random sample of size 40 from a population with standard deviation 2.5....

4 We draw a random sample of size 40 from a population with standard deviation 2.5. Show work in excel with formulas a If the sample mean is 27, what is a 95% confidence interval for the population mean? b If the sample mean is 27, what is a 99% confidence interval for the population mean? c If the sample mean is 27, what is a 90% confidence interval for the population mean? d If the sample mean is 27...

The sample variance of a random sample of 50 observations from a normal population was found...

The sample variance of a random sample of 50 observations from a normal population was found to be s2 = 80. Can we infer at the 1% significance level (i.e., a = .01) that the population variance is less than 100 (i.e., x < 100) ? Repeat part a changing the sample size to 100 What is the affect of increasing the sample size?

7.A random sample of 49 observations is drawn from a population with a normal distribution. If...

7.A random sample of 49 observations is drawn from a population with a normal distribution. If the sample mean is 265 and the sample standard deviation is 57, find the 95% confidence interval for the population mean. 8. A random sample of 49 observations is drawn from a population with a normal distribution with a standard deviation of 57. If the sample mean is 265, find the 95% confidence interval for the population mean. Compare this confidence interval with the...

Suppose we take a random sample X1,…,X5 from a normal population with unknown variance σ2 and...

Suppose we take a random sample X1,…,X5 from a normal population with unknown variance σ2 and unknown mean μ. We test the hypotheses H0:σ=2 vs. H1:σ<2 and we use a critical region of the form {S2<k} for some constant k. (1) - Determine k so that the type I error probability α of the test is equal to 0.05. (2) - For the value of k found in part (1), what is your conclusion in this test if you see...

Suppose we take a random sample X1,…,X5 from a normal population with an unknown variance σ2...

Suppose we take a random sample X1,…,X5 from a normal population with an unknown variance σ2 and unknown mean μ. Construct a two-sided 95% confidence interval for σ2 if the observations are given by −1.25,1.91,−0.09,2.71,2.70

Suppose we take a random sample X1,…,X7 from a normal population with an unknown variance σ21...

Suppose we take a random sample X1,…,X7 from a normal population with an unknown variance σ21 and unknown mean μ1. We also take another independent random sample Y1,…,Y6 from another normal population with an unknown variance σ22 and unknown mean μ2. Construct a two-sided 90% confidence interval for σ21/σ22 if the observations are as follows: from the first population we observe 3.50,0.64,2.68,6.32,4.04,1.58,−0.45 and from the second population we observe 1.85,1.53,1.57,2.13,0.74,2.17

Subjects