Question

Please criticize the following statement regarding the interpretation of a confidence interval: Results for a 95%...

Please criticize the following statement regarding the interpretation of a confidence interval:

Results for a 95% Confidence Interval for estimating the population mean: 74.1< Mean< 83.1

" After looking at the above results we can conclude that there is a 95% chance that the confidence interval contains the true mean of the population"

Is the above statement correct? Why? If it is not correct how can we re-state the conclusion in order to interpret correctly the above confidence interval?

Homework Answers

Answer #1

Yes, the above statement is correct, because we are given a 95% confidence interval for the population mean and we can interpret as 95% chance or probability of founding or getting population mean is the given confidence interval. For the given confidence interval, we are 95% confident that the population mean will lies between 74.1 and 83.1. We constructed the confidence interval for the population mean based on the sample data by using sample mean, sample standard deviation, and sample size. We use particular confidence level during the construction of confidence interval. For this scenario we use 95% confidence level. The 95% confidence level indicate that we are 95% confident or there is a 95% possibility or chance or probability of population mean being lies between lower and upper limit of confidence interval.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Question 1. Which of the following is the CORRECT interpretation of a 95% confidence interval? a)...
Question 1. Which of the following is the CORRECT interpretation of a 95% confidence interval? a) There is a 95% probability that the interval contains the population value b) There is a 95% chance that the true population value is inside the interval c) if we sampled from a population repeatedly and created confidence intervals, 95% of those confidence intervals would contain the population mean d) We are 95% sure of the sample statistic Question 2. What is the mean...
1 - Which of the following statements is true regarding a 95% confidence interval? Assume numerous...
1 - Which of the following statements is true regarding a 95% confidence interval? Assume numerous large samples are taken from the population. a. In 95% of all samples, the sample proportion will fall within 2 standard deviations of the mean, which is the true proportion for the population. b. In 95% of all samples, the true proportion will fall within 2 standard deviations of the sample proportion. c. If we add and subtract 2 standard deviations to/from the sample...
Utilize the following information and answer the questions below: A 95% confidence interval obtained from a...
Utilize the following information and answer the questions below: A 95% confidence interval obtained from a sample of 100 outpatients for the true population mean normal mean systolic blood pressure is given by (114 mmHG, 120 mmHG). Construct the confidence interval. Provide a correct interpretation of this interval. Can you think of other interpretations that would also be correct? This confidence interval came from a single sample, would we get the same interval if we obtained a different set of...
Use the standard normal distribution or the​ t-distribution to construct a 95% confidence interval for the...
Use the standard normal distribution or the​ t-distribution to construct a 95% confidence interval for the population mean. Justify your decision. If neither distribution can be​ used, explain why. Interpret the results. In a random sample of fortyone ​people, the mean body mass index​ (BMI) was 27.7 and the standard deviation was 6.24 Which distribution should be used to construct the confidence​ interval? Choose the correct answer below. (Use a t-distribution because the sample is random n>=30, and o is...
11. The correct interpretation of 95% confidence is (Circle one): a) We can be 95% confident...
11. The correct interpretation of 95% confidence is (Circle one): a) We can be 95% confident that the interval includes the sample mean. b) 95% of all possible population means will be included in the interval. c) 95% of the possible sample means will be included in this interval. d) The method used to get the interval, when used over and over, produces intervals which include the true population mean 95% of the time. 12. Suppose a two-sided (or two-tailed)...
3. A sample of 95 results in 57 successes. Use Table 1. Please do not post...
3. A sample of 95 results in 57 successes. Use Table 1. Please do not post if you are unsure. THANK YOU! a. Calculate the point estimate for the population proportion of successes. (Do not round intermediate calculations. Round your answer to 3 decimal places.) POINT ESTIMATE 0.600 (CORRECT)    b. Construct 99% and 90% confidence intervals for the population proportion. (Round intermediate calculations to 4 decimal places. Round "z-value" and final answers to 3 decimal places.) Confidence Level Confidence...
State how you would respond to the following student posts in a discussion on how to...
State how you would respond to the following student posts in a discussion on how to interpret a 95% confidence interval for a population mean. One student posted their interpretation as “There is a 95% chance that this population mean will fall inside the confidence interval.” Another student responded to this post with “I don’t think that your interpretation is correct. The population mean is a fixed value. There is no chance involved. The population mean either falls inside the...
State how you would respond to the following student posts in a discussion on how to...
State how you would respond to the following student posts in a discussion on how to interpret a 95% confidence interval for a population mean. One student posted their interpretation as “There is a 95% chance that this population mean will fall inside the confidence interval.” Another student responded to this post with “I don’t think that your interpretation is correct. The population mean is a fixed value. There is no chance involved. The population mean either falls inside the...
A random sample of n individuals were selected. A 95% confidence interval ($52,000 to $70,000) was...
A random sample of n individuals were selected. A 95% confidence interval ($52,000 to $70,000) was constructed using the sample results. Which of the following statement(s) is/are true? (Can choose answer more than 1) If all possible samples of size n were drawn from this population, about 95% of the population means would fall in the interval ($52,000 to $70,000). We do not know for sure whether the population mean is in the interval $52,000 and $70,000. If all possible...
A random sample of n individuals were selected. A 95% confidence interval ($52,000 to $70,000) was...
A random sample of n individuals were selected. A 95% confidence interval ($52,000 to $70,000) was constructed using the sample results. Which of the following statement(s) is/are true? ( Can choose more than one answer) If all possible samples of size n were drawn from this population, about 95% of the population means would fall in the interval ($52,000 to $70,000). We do not know for sure whether the population mean is in the interval $52,000 and $70,000. If all...