1. A confidence interval for a population mean has a margin of error of 3.8. a) Determine the length of the confidence interval. b) If the sample mean is 55.8, obtain the confidence interval. Confidence interval: (__?__ ,__?___ ). 2. A confidence interval for a population mean has length 20. a) Determine the margin of error. b) If the sample mean is 58, obtain the confidence interval. Confidence interval: ( __?__,__?__ ). 3. A random sample of n measurements was selected from a population with unknown mean and standard deviation . Calculate a 95 % confidence interval for for each of the following situations: (a) n=105, x=31.4, s=2.75 (b) n=90, x=86.5, s=3.51 (c) n= 80, x=66.8, s=4.72 (d) n=120, x=100.7, s=2.65 4. The following random sample was selected from a normal distribution: 1 1 2 1 1 1 1 54 4 3 3 0 5 6 9 13 1 13 5 4 20 15 4 16 19 (a) Construct a 90% confidence interval for the population mean . (b) Construct a 95% confidence interval for the population mean . 5. The air in poultry-processing plants often contains fungus spores. Inadequate ventilation can affect the health of the workers. The problem is most serious during the summer. To measure the presence of spores, air samples are pumped to an agar plate and "colony-forming units (CFUs)" are counted after an incubation period. Here are data from two locations in a plant that processes 37,000 turkeys per day, taken on four days in the summer. The units are CFUs per cubic meter of air. Day Day Day Day 1 2 3 4 Kill room 3175 2526 1763 1090 Processin 529 141 362 224 g The spore count is clearly higher in the kill room. Give sample means and a 99.5% confidence interval to estimate how much higher the spore count is in the kill room. To do this problem correctly you need to think carefully about whether this is really a matched pairs design (one sample with two measurement) or a two sample design. X bar (kill): ______ X bar (processing): _______ 99.5% confidence interval: _____ to _____ 6. The point of this problem is to get you used to using the table of critical values to do hypothesis tests when you don't have software available that will calculate the precise P-value associated to your test statistic. A sample of 9 measurements, randomly selected from a normally distributed population, resulted in a sample mean, x=5.2 and sample standard deviation s=1.94. Using =0.05, test the null hypothesis that the mean of the population is =7.2 against the alternative hypothesis that the mean of the population satisfies <7.2. Find: (a) the degree of freedom ________ (b) the critical t value _________ (To do this you will need to use the degree of freedom and the significance level to find the critical value in the table). (c) the t test statistic _________ 7. The point of this problem is to get you used to using the table of critical values to do hypothesis tests when you don't have software available that will calculate the precise P-value associated to your test statistic. Test the claim that for the population of statistics final exams, the mean score is =78. Sample statistics include n=29, x=79, and s=14. Use a significance level of =0.02. (a) The t test statistic is ________ (b) The positive critical value t is _________ (To find critical values you will need to use the degree of freedom and the significance level to find the critical value in the table of critical values. You will also have to take into account whether this is a one-sided or two-sided test.) (c) The negative critical value is _________ 8. This problem asks you to do hypothesis testing without calculating precise P-values but using the table of critical values from your textbook instead. One of the most feared predators in the ocean is the great white shark. It is known that the white shark grows to a mean length of 19 feet; however, one marine biologist believes that great white sharks off the Bermuda coast grow much longer. To test this claim, full-grown white sharks were captured, measured, and then set free. However, this was a difficult, costly and very dangerous task, so only four sharks were actually sampled. Their lengths were 20, 20, 23,and 25 feet. Do the data provide sufficient evidence to support the claim? Use =0.01 (a) t test statistic ____________ (b) critical value t= ___________ 9.) This problem asks you to do hypothesis testing without calculating precise P-values but using the table of critical values from your textbook instead. The effectiveness of a new bug repellent is tested on 11 subjects for a 10 hour period. Based on the number and location of the bug bites, the percentage of surface area exposed protected from bites was calculated for each of the subjects. The results were as follows: X bar =85 %, s=9% The new repellent is considered effective if it provides a percent repellency of at least 91. Using =0.05, construct a hypothesis test with null hypothesis =0.91 and alternative hypothesis >0.91 to determine whether the mean repellency of the new bug relellent is greater than 91 by computing the following: (a) the degree of freedom _________ (b) the critical t value _______ (c) the t test statistic is ________ 10. This problem asks you to do hypothesis testing without calculating precise P-values but using the table of critical values from your textbook instead. When a poultry farmer uses his regular feed, the newborn chickens have normally distributed weights with a mean of 61.7 oz. In an experiment with an enriched feed mixture, ten chickens are born with the following weights (in ounces). 64. 63. 69. 6 65. 6 64. 66. 65. 66. 2 9 3 5 7 4 3 7 1 5 Use the =0.05 significance level to test the claim that the mean weight is higher with the enriched feed. (a) The sample mean is x bar= __________ (b) The sample standard deviation is s= _______ (c) The test statistic is t= ________ (d) The critical value is t= ________ To test the efficacy of a new cholesterol-lowering medication, 10 people are selected at random. Each has their LDL levels measured (shown below as Before), then take the medicine for 10 weeks, and then has their LDL levels measured again (After). Subjec Befor Afte t e r 1 133 108 2 132 136 3 175 153 4 160 174 5 182 195 6 183 184 7 143 110 8 127 117 9 145 147 10 166 131 Give a 97.9% confidence interval for BA, the difference between LDL levels before and after taking the medication. Confidence Interval = _________ at 97.9% confidence