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- From: Mathematics, Statistics and Probability
- Posted on: Tue 19 Jan, 2016
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1. Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis. A= 0.05 for a left-tailed test.
Find the value of the test statistic z using z = P-P/?pq/n The claim is that the proportion of accidental
2. deaths of the elderly attributable to residential falls is more than 0.10, and the sample statistics include n = 800 deaths of the elderly with 15% of them attributable to residential falls.
3. Use the given information to find the P-value. Also, use a 0.05 significance level and state the conclusion about the null hypothesis (reject the null hypothesis or fail to reject the null hypothesis). The test statistic in a right-tailed test is z = 1.43.
4. Find the number of successes x suggested by the given statement. Among 720 people selected randomly from among the residents of one city, 13.89% were found to be living below the official poverty line.
5. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the z test statistic for the hypothesis test. A random sampling of sixty pitchers from the National League and fifty-two pitchers from the American League showed that 19 National and 11 American League pitchers had E.R.A's below 3.5.
6. Assume that you plan to use a significance level of alpha = 0.05 to test the claim that p1 = p2. Use the given sample sizes and numbers of successes to find the P-value for the hypothesis test. n1 = 50; n2 = 50x1 = 8; x2 = 7
7. Construct the indicated confidence interval for the difference between population proportions . Assume that the samples are independent and that they have been randomly selected. In a random sample of 300 women, 49% favored stricter gun control legislation. In a random sample of 200 men, 28% favored stricter gun control legislation. Construct a 98% confidence interval for the difference between the population proportions p1 - p2.
8. Construct the indicated confidence interval for the difference between the two population means. Assume that the two samples are independent simple random samples selected from normally distributed populations. Also assume that the population standard deviations are equal (sigma1 = sigma2), so that the standard error of the difference between means is obtained by pooling the sample variances. A researcher was interested in comparing the resting pulse rates of people who exercise regularly and people who do not exercise regularly. Independent simple random samples were obtained of 16 people who do not exercise regularly and 12 people who do exercise regularly. The resting pulse rate (in beats per minute) of each person was recorded. The summary statistics are as follows
Do not Exercise | Does Exercise
X1=73.4 beats/per min X2=69.7 beats/per min
S1=10.3 beats/per min S2=8.6 beats/ per min
N1=16 N2=12
Construct a 90% confidence interval for the difference between the mean pulse rate of people who do not exercise regularly and the mean pulse rate of people who exercise regularly.
9. The two data sets are dependent. Find d= to the nearest tenth x=11.2, 11.3,11.6,12.9, 10.6.
Y=11.1, 12.6, 12.9, 10.7, 13.3
10. Given the linear correlation coefficient r and the sample size n, determine the critical values of r and use your finding to state whether or not the given r represents a significant linear correlation. Use a significance level of 0.05. r = 0.843, n = 5
11. Find the value of the linear correlation coefficient r. The paired data below consist of the test scores of 6 randomly selected students and the number of hours they studied for the test. Hours= 5, 10, 4, 6, 10, 9…..Score=64,86,69,86,59,87
12. Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level alpha. n = 17, alpha = 0.05
13. Use the given data to find the best predicted value of the response variable.
Nine pairs of data yield r=0.867 and the regression equation y=19.4 + 0.93x. Also, y=64.7. What is the best predicted value of y for x=50?
14. Use the given data to find the equation of the regression line. Round the final values to three significant digits, if necessary. Two different tests are designed to measure employee productivity and dexterity. Several employees are randomly selected and tested with these results. Productivity 23, 25,28,21,21,25,26,30,34,36 Dexterity 49, 53,59,42,47,53,55,63,67,75
15. Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 130.3, the explained variation is 79.3, and the unexplained variation is 51. Find the coefficient of determination.
16. Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the value of the test statistic.
17. Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. Identify the p-value
18. Given below are the analysis of variance results from a Minitab display. Assume that you want to use a 0.05 significance level in testing the null hypothesis that the different samples come from populations with the same mean. What can you conclude about the equality of the population means?
19. Provide an appropriate response. Which of the following nonparametric tests reaches a conclusion equivalent to the Mann-Whitney U test?
Wilcoxon rank-sum test
sign test
Wilcoxon signed-ranks test
Kruskal-Wallis test
20. Find the critical value. Assume that the test is two-tailed and that n denotes the number of pairs of data. n =80, alpha = 0.05
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