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1. The probability distribution shown here describes a population of measurements that can assume values of 4, 5, 6, and 7, each of which occurs with the same relative frequency (1/4).
2. Suppose a random sample of n=16 measurements is selected from a population with mean and standard deviation. For each of the following values of mean and standard deviation give the values of mean- and standard deviation-.
a. mean 5, st.dev.3; b. mean 25, st.dev. 16; c. mean 10, st. dev.32; d. mean 5, st.dev. 88.
3. A random sample of n=100 observations is selected from a population with mean 29 and st. dev. 18. Approximate the probabilities shown below:
a. P(x>equal 28); b. P(22.1
4. The average salary for a certain profession is $82,000. Assume that the standard deviation of such salaries is $39,000. Consider a random sample of 59 people in this profession and let x represent the mean salary for the sample.
5. A random sample of 92 obseravtions produced a mean x=25.4 and a standard deviation s=2.7. Find a 95%, 90%, and 99% confidence interval.
6. The mean and standard deviation of a random sample of n measurements are equal to 34.2 and 3.3, respectively.
a. Find a 95% confidence interval if n=81; b. find a 95% confidence interval if n=324; c. Find the widths of the confidence intervals found in parts a and b.
7. The random sample shown below was selected from a normal distribution. 5,8,5,7,8,3.
8. For the binomial sample information summarized below indicate whether the sample size is large enough to use the large sample approximation to construct a confidence inerval for p. n=20, p=0.50.
9. A newspaper reported that 70% of people say that some coffee shops are overpriced. The source of this information was a telephone survey of 100 adults.
a. Identify the population of interest.
b. Identify the sample for the study.
c.Identify the parameter of interest.
d. Find and interpret the 90% confidence interval.
10. 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 varied their excersises, group 2 performed the same exersice, and group 3 had no set schedule. a.16 people had dropped out of the first group Estimate the dropout rate of the first group, use 95% confidence interval. b. 20 people had dropped out of the third group. Estimate the dropout rate and use 95% confidence interval.
11. If you wish to estimate the population mean with a sampling distribution error SE=0.25 using a 95% confidence interval and you know from prior sampling that variance is equal to 8.3, how many obseravtions would have to be included in your sample?
12. Suppose N=90,000, n=22,500, and and s=50.
a. compute the standard error of x using the finite population correction factor.
b. Repeat part a assuming n=45,000.
c. Repeat part a assuming n=90,000.
d. Compare parts a, b, and c and describe what happens to the standard error of x as n is increased.
13. Suppose you want to estimate a population proportion,p, and p=0.41, N=6,100, and n=1,900. Find an approximate 95% confidence interval for p.
14. A random sample of size n=20 was drawn from a population of size N=200. The measurements shown in a table to the right were obtained:
a. Estimate mean with an approximate 95% confidence interval.
b. Estimate p, the proportion of measurements in the population that are greater than 30 with an approximate 95% confidence interval.
15. In order to evaluate the reasonableness of a firm's stated total value of its parts inventory, an auditor randomly samples 50 of the total 400 parts in stock, prices each part, and reports the results shown in the table.
|Part Price||Sample Size|
a. Give a point estimate of the mean value of the parts inventory.
b. Find the estimated standard error of the point estimate of part a.
c. The author estimates the mean value of the parts to be in the interval ... with 95% confidence.
d. The firm reported the mean parts inventory value of $55. What does the confidence interval of part c suggest about the reasonableness of the firm's reported figure?
10. Researchers conducted a study of variety in exercise workouts. A sample of 120 men and women were randomly divided into three groups