Question 1
Do this problem by hand. All answers should be integers (no decimal places).
The mean sales per customer µ for all of the sales for your company last month is not known. Based on your past experience, you are willing to assume that the population standard deviation of sales, σ, is about $220. If you take a random sample of 100 sales, what is the value of the standard error of x¯¯? (Blank #1).
If you take a random sample of 25 sales, what is the value of the standard error for x¯¯? (Blank #2).
Remember that the sampling distribution of x¯¯ is normal with a mean of µ and a standard deviation of σx¯.
Question 2
Suppose we have a population with unknown mean, μ, and standard deviation, σ=100. We have a sample size of 225 and we estimate a sample mean, x¯¯=30.
The point estimate of μ is ______ (Blank #1, no decimal places).
Create a 95% confidence interval for μ using the value 1.96 from the normal probability distribution, [Blank #2, Blank #3]. Use two decimal places.
Question 3Which statement is true? The 95% confidence interval is wider than the 90% confidence interval because
Question 3 options:
a) the standard error for the 95% interval is bigger than for the 90% interval.
b) we can only be more confident in the estimate if we include more possible values for the population mean.
c) the margin of error for the 90% interval is bigger than for the 95% interval.
d) there's a higher probability of 95% confidence interval containing the mean than the 90% confidence interval containing the mean.
Question 4As the sample size increased, the width of the confidence interval got smaller. Why?
Question 4 options
a) In general, the more data we have, the more accurate our estimate will be.
b) The standard deviation is smaller when N is larger.
c) The mean is smaller when N is larger.
d) When we increased N, we changed the t-value that we used.
Question 5
A 95% confidence interval for the mean μ of a population is computed from a random sample and found to be 9 ± 3. We may conclude
Question 5 options:
A.there is a 95% probability that μ is between 6 and 12.
B.there is a 95% probability that the true mean is 9 and there is a 95% chance that the true margin of error is 3.
C.if we took many, many additional random samples and from each computed a 95% confidence interval for μ, approximately 95% of these intervals would contain μ.
D.all of the above.
Question 6.
We create a 90% confidence interval [61,81] for the population mean. What is the value of x¯¯?
Question 7
Suppose we estimate a 90% confidence interval, [64, 81]. What is the margin of error?