Question

1. A random sample of n measurements was selected from a population with standard deviation σ=13.6 and unknown mean μ. Calculate a 90 % confidence interval for μ for each of the following situations:

(a) n=45, x¯¯¯=89.8 ≤μ≤

(b) n=70, x¯¯¯=89.8 ≤μ≤

(c) n=100, x¯¯¯=89.8 ≤μ≤

(d) In general, we can say that for the same confidence level, increasing the sample size the margin of error (width) of the confidence interval. (Enter: ''DECREASES'', ''DOES NOT CHANGE'' or ''INCREASES'', without the quotes.)

2. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 129 people living in Gastown and finds that 20 have an annual income that is below the poverty line. Part ii) Use the sample data to compute a 95% confidence interval for the true proportion of Gastown residents living below the poverty line. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places). 95% confidence interval = ( , )

3. A government official is in charge of allocating social programs throughout the city of Vancouver. He will decide where these social outreach programs should be located based on the percentage of residents living below the poverty line in each region of the city. He takes a simple random sample of 120 people living in Gastown and finds that 21 have an annual income that is below the poverty line. Suppose that the government official wants to re-estimate the population proportion and wishes for his 95% confidence interval to have a margin of error no larger than 0.03. How large a sample should he take to achieve this? Please carry answers to at least six decimal places in intermediate steps. Sample size =

4. A poll is taken in which 316 out of 575 randomly selected voters indicated their preference for a certain candidate.
(a) Find a 9898% confidence interval for pp. (  ≤ p ≤ )
(b) Find the margin of error for this 9898% confidence interval for p.
(c) Without doing any calculations, indicate whether the margin of error is larger or smaller or the same for an 80% confidence interval.
A. larger
B. smaller
C. same

5. A random sample of 9 size AA batteries for toys yield a mean of 3.62 hours with standard deviation, 0.94 hours.

(a) Find the critical value, t*, for a 99% CI. t* =

(b) Find the margin of error for a 99% CI.

Answer 1