a sample of 15 one-pound jars of coffee of Brand I showed that the mean amount of caffeine in these jars is 80 milligrams per jar with a standard deviation of 5 milligrams. Another sample of 12 one-pound coffee jars of Brand II gave a mean amount of caffeine equal to 77 milligrams per jar with a standard deviation of 6 milligrams. Construct a 95% confidence interval for the difference between the mean amounts of caffeine in one-pound coffee jars of these two brands. Assume that the two populations are normally distributed and that the standard deviations of the two populations are not equal.
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- A study was conducted that measured the total brain volume (TBV) (in mm³) of patients that had schizophrenia and patients that are considered normal. The first table contains the TBV of the non- schizophrenic patients and the second table contains the TBV of schizophrenia patients. Compute a 99% confidence interval for the difference in TBV of non-schizophrenic patients and patients with Schizophrenia. Prior studies say nothing about the equality of variances. Round to the nearest whole number. Total Brain Volume (in mm³) of Non-Schizophrenic Patients 1487997 1611227 1527495 1409812 1297379 1400278 1724615 1249097 1309037 1546157 1352710 1620645 1446958 1540957 1535216 1303042 1363737 1318121 1460479 1602502 1353583 1292976 1558222 1474289 1541397 1373993 1398046 1282528 1516312 1567897 1532468 1381812 Total Brain Volume (in mm³) of Schizophrenia Patients 1653156 1037545 1063003 1287704 1262253 1455977 1438274 1280706 1451005 1283081 1214368 1536994 1082431 1372061 1096716 1699683…Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 12 people with the illness, and the second group consisted of 14 people with the illness. The first group received treatment 1 and had a mean time until remission of 166 days with a standard deviation of 8 days. The second group received treatment 2 and had a mean time until remission of 163 days with a standard deviation of 9 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 90% confidence interval for the difference −μ1μ2 between the mean number of days before remission after treatment 1 ( μ1 ) and the mean number of days before remission after treatment 2 ( μ2 ). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate…The average daily intake of dietary fiber for a random sample of 53 young male adults (ages 19-49) is 9.05 grams/day with a standard deviation of 0.04 grams/day. Construct a 95% confidence interval for the average daily intake of dietary fiber for male young adults and compute its width.
- Researchers interested in determining the relative effectiveness of two different drug treatments on people with a chronic illness established two independent test groups. The first group consisted of 15 people with the illness, and the second group consisted of 11 people with the illness. The first group received treatment 1 and had a mean time until remission of 187 days with a standard deviation of 6 days. The second group received treatment 2 and had a mean time until remission of 162 days with a standard deviation of 8 days. Assume that the populations of times until remission for each of the two treatments are normally distributed with equal variance. Construct a 90% confidence interval for the difference H₁-H₂ between the mean number of days before remission after treatment 1 (H₁) and the mean number of days before remission after treatment 2 (H₂). Then find the lower limit and upper limit of the 90% confidence interval. Carry your intermediate computations to at least three…A research firm supplies manufacturers with estimates of the sales of their products from samples of stores. Marketing managers often look at the sales estimates and ignore sampling error. An SRS of 50 stores this month shows mean sales of 41 units of a particular appliance with standard deviation of 11 units. During the same month last year, an SRS of 52 stores gave mean sales of 38 units of the same appliance with a standard deviation of 13units. An increase from 38to 41 is a rise of 7.9%.. The marketing manager is happy because sales are up 7.9%. (a) Give a 95%confidence interval for the difference in mean number of units of the appliance sold at all retail stores. Give your answers to three decimal places. lower bound: upper bound:The mean and standard deviation of system blood pressure of 200 employees in a factory were 127mmhg and 13 mmHg respectively. Calculate and interprete the 95% confidence interval of systolic blood pressure of the employees
- A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 42 households from the city, which gave the mean water usage to be 3409.30 gallons over a one-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is 387.90 gallons. Make a 97% confidence interval for the average monthly residential water usage for all households in this city.A random sample of 50 students taken from ABC high school showed that they spent 6.1 hours per day for playing computer games on the average with a standard deviation of 3.2 hours per day. Estimate the true average hours per day spent for playing computer games by the ABC high school students.A peditrician claimed that the average time for a drug to take effect is 15 minutes with standard deviation of eight minutes. In sample of 49 trials the average time was 18 minutes. Test the claim of a pediatrician that the average time is not equal to 15 minutes. Assume the the average time for a drug to take effect is approximately normal distributed
- A researcher is comparing the amount of calories in two different lunch special pizzas: Hawaiian and pepperoni. Random samples of 30 Hawaiian and 30 pepperoni are taken. The mean amount of calories in the Hawaiian pizza was 800 calories with a standard deviation of 50 calories and the mean amount of calories in the pepperoni pizza was 1000 with a standard deviation of 100 calories. The population standard deviations are unknown but considered to be equal. What is the 99% confidence interval for the difference between the two population means? O Confidence Interval - (800- - 1000) ± 2.576₁ (50)² 30 Confidence Interval= (800-1000) + (2.663) (79.06, Confidence Interval=(800-1000) ± 2.663, (50) 30 Confidence Interval= (800-1000) + (2.576) (79.06. + (100)² 30 1 1 30 30 + (100)² 30 1 1 30 30 + )The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 253.8 and a standard deviation of 61.7. What is the approximate percentage of women with platelet counts between 192.1 and 315.5?A recent study stated that if a person chewed gum, the average number of sticks of gum he or she chewed daily was 8. To test the claim, the researcher selected a random sample of 36 gum chewers and found the mean number of sticks of gum chewed per day was 8. The standard deviation of population is 1. at a = 0. 05, is the number of sticks of gum a person chews per day actually greater than 8. There is not enough evidence to support the claim that average is greater than 8. There is enough evidence to support the claim that average is greater than 8. There is enough evidence to support the claim that average is smaller than 8. There is not enough evidence to support the claim that average is greater than 8.