1) Question 1 (Q3)- a random sample of n=100 observations is selected from a population with µ=30 and o=23. Approximate the probabilities shown below.
a. P(x̄ ≥28
b. P(22.1≤ x̄ ≤ 26.8)
c. P(x̄≤ 28.2)
d. P(x̄≥ 27.0)
2) Question 2 ( Q4)- The average salary from certain profession is $82,000. Assume that the standard deviation of such salaries is $32,000. Consider a random sample of 58 people in the profession and let x represent the mean salary for the sample.
E. find P (x̄ > 72,500 =
3) Question 3 (Q5)- A random sample of 91 Observation produced a mean x̄ = 25.4 and a standard deviations s=2.4.
a. Find a 95% confidence interval for µ (use intervals or decimals for any numbers in the expression. Round to two decimals places as needed.)
b. Find a 90% confidence interval for µ (use intervals or decimals for any numbers in the expression. Round to two decimals places as needed.)
c. Find a 99% confidence interval for µ (use intervals or decimals for any numbers in the expression. Round to two decimals places as needed.)
4) Question 4 (Q6)- The mean and the standard deviation of a random sample of n measurements are equal to 33.4 and 3.9, respectively.
a. Find a 95% confidence interval for µ if n= 144
b. Find a 95% confidence interval for µ if n= 576
c. Find the widths of the confidence intervals found in parts a and b. What is the effect on the width of a confidence interval of quadrupling the sample size while holding the confidence coefficient fixed?
5) Question 5 (Q8)- A newspaper reported that 8% of people say that some coffee shops are overprices. The source of this information was a telephone survey of 500 adults.
d. Find and interpret a 90% confidence interval for the parameter of the interest
( , ).
6) Question6 (Q9)- Researchers conducted a study of variety in exercise workouts. A sample of 120 men and women were randomly divided into three groups, with 40 people per group. Group 1 members varied their exercise routine in workouts, group 2 members performed the same exercise are each workout, and group 3 members had no set schedule or regulation for their work outs.
a. By the end of the study, 18 people had dropped out of the first exercise group. Estimate the dropout rate for exercisers who vary their routine in workouts?
b. By the end of the study, 25 people had dropped out of the third exercise group. Estimate the dropout rate for exercisers who have no set schedule for their workouts. Use a 90% confidence interval and interpret the result.
7) Question 7 ( Q10) –If you wish to estimate a population mean with a sampling distribution error SE=0.32nusing a 95% confidence interval and you know from prior sampling that o2 is approximately equal to 8.3, how many observations would have to be included in your sample?
a. The number of observations that would have to be included in your sample is (round up the nearest observation)
8) Question 8 (Q11)- Suppose N=5,000,n=1,000, and s=50
a. Compute the standard error of x̄ using the finite population correction factor
b. Repeat part assuming n=2,000.
c. Repeat part a assuming n=5,000
d. Compare parts a, b, c , and describe what happens to the standard error of x as n is increased.
9) Question 9 (Q12) – Suppose you want to estimate a population proportion, p, and ̂p=0.31, N=6100, and n=1700. Find an approximate 95% confidence interval for p.
a. An approximate 95% confidence interval for p is + .
10) Question 10 (Q13)- A random sample of size n= 20 was drawn from a population of size N= 220. The measurements shown in the table below were obtained.
40 28 43 22
33 27 47 21
55 40 27 35
18 39 39 36
48 49 53 53
a. Estimate µ with an approximate 95% confidence interval. (round the three decimal places as needed).
b. Estimate p, the proportion of measurements in the population that are greater than 30, with an approximate 95% confidence interval.
11) Question 11( Q14)- The random sample shown below was selected from a normal distribution. 8,8,4,7,7,2
a. Construct a 99% confidence interval for the population mean µ. ( , ) ( round to two decimal places as needed).
b. Assume that sample mean x̄ and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n=25 observations. Repeat part a. what is the effect of increasing the sample size on the width of the confidence intervals.
12) Question 12 (Q15)- in order to evaluate the reasonableness of firm’s stated total value of its parts inventory, as auditor randomly samples 50 of the total 300 parts in stock, process each part, and reports the results shown in the table. Use this information to answer the following question
Part price $52 $90 $12 $57 $98 $85 $70 $99
Sample Size 7 3 10 3 7 6 7 7
a. Give a point estimate of the mean of the value of the parts inventory. $ (round to the nearest cent as needed).
b. Find the estimate standard error of the point estimate of part a.
c. Find the limit