Assignment:
1. Construct a confidence interval for µd the mean differences d for population of paired data. Assume that the population of paired differences is normally distributed. 10 different families are tested for the number of gallons of water a day they use before and after viewing a conservation video. Construct a 90% confidence interval for the mean of differences.
Before 33 33 38 33 35 35 40 40 40
After 34 28 25 28 35 33 31 28 35
2. Assume that the weight loss for the first month of a diet program varies between 6 and 12 pounds, and is spread evenly over the range of possibilities, so that there is a uniform distribution. Find the probability of the given range of pounds lost.
3. Find the d to the nearest tenth for the two sets of independent data.
X 12.9 11.3 10.7 12.9 12.9
Y 12.6 12.6 10.0 10.7 12.3
4. Assume Z is a standard normal variable, find the probability. The probability that Z lies between -1.10 and -0.36.
5. Construct the indicated confidence interval for the differences between populations p1 - p2. Assume that the samples are independent and they have been randomly selected. In a random sample of 500 people aged 20-24, 22% were smokers. In a random sample of 450 people aged 25-29, 14% were smokers. Construct a 95% confidence interval for the difference between the population proportion p1 - p2
6. A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. Find P60, the score which separates the lower 60% from the top 40%.
7. In a vote on the Clean Water bill, 41% of 205 Democrats voted for the bill while 40% of the 230 Republicans voted for it.
8. Find the Margin of error for the 95% confidence interval used to estimate the population proportion.
N = 165, x = 96
9. Find the minimum sample size you should use to assure that your estimate of p will be within the required margin of error and around the population p. Margin of error 0.04; confidence interval 99%; from a prior study, p is estimated by 0.13.
10. Use the confidence level and sample data to find the margin of error E. College students' annual earnings: 99% confidence; n = 74, x = $3967, σ = $874.
11. Use the given degree of confidence and sample data to construct a confidence interval for the population mean µ. Assume that the population has a normal distribution. A sociologist develops a test to measure attitudes about public transportation. 27 randomly selected subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.4. Construct the 95% confidence interval for the mean score of all such subjects.
12. Identify the null hypothesis H0 and the alternative hypothesis H1. A researcher claims that 62% of voters favor gun control.
13. Use the given information to find the p-value. The test statistic in a right-tailed test is z = 1.43.
14. Determine whether the hypothesis test involves a sampling distribution of means that is a normal distribution, student t distribution, or neither.
Claim: µ = 111. Sample data: n = 10, x = 101, s = 15.3. The sample data appear to come from a normally distributed population with unknown µ and σ.
15. Assume that a hypothesis test of the given claim will be conducted. Identify the type I error for the test.
Carter Motor Company claims that its new sedan, the Libra, will average better than 30 miles per gallon in the city. Identify the type I error for the test.
16. Assume the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test the null hypothesis. α = 0.1 for a two-tailed test.
17. Find the number of successes, x, suggested by the given statement.
A computer manufacturer randomly selects 2360 of its computers for quality assurance and finds that 2.54% of these computers are found to be defective.
18. Assume in one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 KWh (kilo watt per hour) and standard deviation of 218 KWh.
If 50 different homes are selected, find the probability that their mean energy consumption level for September is greater than 1075 KWh.
19. A final exam has a mean of 73 with a standard deviation 7.8. If 24 students are randomly selected, find the probability that the mean of their test scores is less than 70.
20. Find the critical value za/2 that corresponds to a degree of confidence of 98%.