Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation...

Assuming the sample size is 30, the sample mean (X) is 24.75, the population standard deviation (σ) is 5, a 95% confidence interval for the population mean would have lower bound of _________________ and upper bound of _______________________.

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 24.75

Population standard deviation = =5

Sample size n =30

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96 ( Using z table )

Margin of error = E = Z/2 * ( / $\sqrt$ n)
=1.96 * (5 / $\sqrt$ 30)

= 1.7892
At 95% confidence interval estimate of the population mean
is,

- E < < + E

24.75 - 1.7892< < 24.75 + 1.7892

22.9608 < < 26.5392
( lower bound= 22.9608 ,upper bound= 26.5392)

orchestra answered 1 year ago

Next > < Previous

Related Solutions

Assuming the sample size is 30, the sample mean (X ̅) is 24.75, the sample standard...

Assuming the sample size is 30, the sample mean (X ̅) is 24.75, the sample standard deviation (s) is 5, and degrees of freedom are 29, a 95% confidence interval for the population mean would have lower bound of _________________ and upper bound of _______________________

Sample size = 10. Population is normal. The sample mean is 1.3 million. Sample standard deviation...

Sample size = 10. Population is normal. The sample mean is 1.3 million. Sample standard deviation is 0.9million. Alpha ( level of significance) is 1%. Ho: Mu > or equal to 1.5 million Ha: Mu< 1.5 million a. What is the critical value? B. What is the test statistics t score? C . Do you reject or accept the null hypothesis?

A sample of size 81 is taken from a population with unknown mean and standard deviation...

A sample of size 81 is taken from a population with unknown mean and standard deviation 4.5. In a test of H0: μ = 5 vs. Ha: μ < 5, if the sample mean was 4, which of the following is true? (i) We would fail to reject the null hypothesis at α = 0.01. (ii) We would fail to reject the null hypothesis at α = 0.05. (iii) We would fail to reject the null hypothesis at α =...

X has a distribution with mean = 70 and standard deviation = 20. The sample size...

X has a distribution with mean = 70 and standard deviation = 20. The sample size is 16. Find P(66 < or equal to x bar < or equal to 71)

Assuming this right skewed population distribution had a population mean of 14.05 and a standard deviation of 11.83; calculate the probability that, in a random sample of 30, the mean of the sample is greater than 16.

a) Assuming this right skewed population distribution had a population mean of 14.05 and a standard deviation of 11.83; calculate the probability that, in a random sample of 30, the mean of the sample is greater than 16. First, draw a picture with the mean labeled, shade the area representing the desired probability, standardize, and use the Standard Normal Table (Table 2 in your text) to obtain this probability. Please take a picture of your hand drawn sketch and...

Item Sample Mean 1 Population standard deviation of 1 n1 Sample Mean 2 Population Standard Deviation...

Item Sample Mean 1 Population standard deviation of 1 n1 Sample Mean 2 Population Standard Deviation 2 n2 7 18 6 169 12 12 121 0.01 Perform a Two-tailed hypothesis test for two population means.

A simple random sample of size 44 has mean 3.01. The population standard deviation is 1.51....

A simple random sample of size 44 has mean 3.01. The population standard deviation is 1.51. Construct a 90% confidence interval for the population mean. 1.The parameter is the population (choose one) mean, standard deviation, proportion, variance 2. The correct method to find the confidence interval is the (choose one) z, t, chi square method

A population has a standard deviation of 25 and a mean of 300. Given a random sample of size 100, how likely is it that the sample mean will be within +/- 5 of the population mean?

1. For a sample, the mean is 34.2, standard deviation is 5.3, and the sample size...

1. For a sample, the mean is 34.2, standard deviation is 5.3, and the sample size is 35. a.) what is the point estimate for the population mean? b.) compute a 95% confidence interval about the mean for the data (use t table) c.) compute a 99% confidence interval about the mean (use t table) 2. a poll asked 25 americans "during the past year how many books did you read?" the mean # was 18.8 books, and stand deviation...

A simple random sample of size 33 has mean x = 14.3 . The population standard...

A simple random sample of size 33 has mean x = 14.3 . The population standard deviation is σ = 3.72 . Can you conclude that the population mean differs from 10 ? The population standard deviation ▼(Choose one) known. The sample size n ▼(Choose one) greater than 30 . The correct decision is to ▼(Choose one). Part 2 of 3 A simple random sample of size 13 has mean x = 7.26 and the standard deviation is s =...

Subjects