Question

Suppose you have selected a random sample of ?=14 measurements from a normal distribution. Compare the standard normal ? values with the corresponding ? values if you were forming the following confidence intervals.

(a)    90% confidence interval
z=

t=

(b)    95% confidence interval
z=  
t=

(c)    98% confidence interval
?=

t=

2) A confidence interval for a population mean has length 20.

a) Determine the margin of error.

b) If the sample mean is 58.6, obtain the confidence interval.
Confidence interval: ( , )

3)The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 14. A random sample of 430 salespeople was taken and the mean number of cars sold annually was found to be 74. Find the 90% confidence interval estimate of the population mean.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

Confidence Interval =

4) A medical researcher wants to investigate the amount of time it takes for patients' headache pain to be relieved after taking a new prescription painkiller. She plans to use statistical methods to estimate the mean of the population of relief times. She believes that the population is normally distributed with a standard deviation of 20 minutes. How large a sample should she take to estimate the mean time to within 4 minutes with 98% confidence?

Sample Size =

An online used car company sells second-hand cars. For 30 randomly selected transactions, the mean price is 2000 dollars.

Part a) Assuming a population standard deviation transaction prices of 190 dollars, obtain a 99% confidence interval for the mean price of all transactions. Please carry at least three decimal places in intermediate steps. Give your final answer to the nearest two decimal places.

Confidence interval: (. , )

Answer 1