If one were to use a standard normal distribution instead of Student's t distribution to calculate a confidence interval, what would be the "critical normal value" used as the coefficient for the s.e.m for a 90% CI?
Solution :
At 90% confidence level the z is ,
= 1 - 90% = 1 - 0.90 = 0.10
/ 2 = 0.10 / 2 = 0.05
Z
/2
= Z 0.05 = 1.645
Critical normal value = 1.645
If one were to use a standard normal distribution instead of Student's t distribution to calculate...
Student's t Distribution CI The manager of The Cheesecake Factory in Boston would like to know the mean number of customers served on weekdays. She believes that the number of customers served follows a Normal distribution. She reports that on six randomly selected weekdays an average of 158.3 customers were served with a sample standard deviation of 52.2. a. Calculate the standard error of the sample mean. b Find the t-critical value for a 99% confidence interval with a sample...
Use the standard normal distribution or the t-distribution to construct a 90% 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 14 mortgage institutions, the mean interest rate was 3.44% and the standard deviation was 0.49%. Assume the interest rates are normally distributed. Which distribution should be used to construct the confidence interval? select a choice below A. Use a t-distribution because the interest...
Use the standard normal distribution or the t distribution to construct a 9 % confidence interval for the population mean Justify your decision if neither distribution can be used, explain why Interpret the results ln a random sample of 17 mortgage institutions, the mean interest rate was 3.69% and the standard deviation was 36% Assume the iterest rates are normally distributed Which distribution should be used to construct the confidence interval? ○ A. Use a t-distribution because it is a...
Use the standard normal distribution or the t-distribution to construct a 90% 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 13 people, the mean length of stay at a hospital was 6.9 days. Assume the population standard deviation is 2.1 days and the lengths of stay are normally distributed. Which distribution should be used to construct the confidence interval? A. Use a normal...
You should use the Student's t-distribution instead of the normal when A The sample size is smaller than 30 B The sample size is larger than 30 C A student is doing the calculations D The degrees of freedom is infinity.
Use the standard normal distribution or the t-distribution to construct the indicated confidence interval for the population mean of each data set. Justify your decision. If neither distribution can be used, explain why. Interpret the results. (a) In a random sample of 36 patients, the mean waiting time at a dentist’s office was 24 minutes and the standard deviation was 7.5 minutes. Construct a 90% confidence interval for the population mean. (b) In a random sample of 25 cereal boxes,...
Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.27. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 2.9 8.4 7.2 4.3 6.8 2.7 7.2 4.8...
Use the standard normal distribution or the t-distribution to construct a 99% confidence interval for the population mean. Justify your decision. If neither distribution can be used, explain why. Interpret the results. In a recent season, the population standard deviation of the yards per carry for all running backs was 1.21. The yards per carry of 25 randomly selected running backs are shown below. Assume the yards per carry are normally distributed. 3.2 6.8 6.1 3.6 6.3 7.1 6.4 5.5...
Use the standard normal distribution or the t-distribution to construct a 99% 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 48 people, the mean body mass index (BMI) was 26.1 and the standard deviation was 6.06. Which distribution should be used to construct the confidence interval? Choose the correct answer below.
This Quiz: 22 pts possit Use the standard normal distribution or the t-distribution to construct a 99% 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 40 people, the mean body mass index (BMI) was 26.9 and the standard deviation was 6.03. O A. Use a normal distribution because the sample is random, the population is normal, and is known O B. Use a...