1. Selasphorus platycerus is a scientific name of the broad-tailed hummingbird that is commonly found throughout the western United States. It is known that the mean incubation time for eggs of this bird is 16.5 days (The Hummingbird Book b y Stokes and Little). However for higher elevations, it is thought that the average incubation time might be different from 16.5 days. A number of broad-tailed hummingbird nests were located in mountain country above 8000 feet, and incubation times for 18 eggs revealed a mean incubation time of 17.83. Assume that the population standard deviation is known to be 2.20.

1. A hospital reported that the normal death rate for patients with extensive burns (more than 40% of the skin area) has been significantly reduced by the use of new fluid plasma compress. Before the new treatment, the mortality rate for extensive bu rn patients was about 60%. Using the new compresses, the hospital found that only 40 of 90 patients with extensive burns died.

1. Construct a 95% confidence interval for the true proportion of the patients who would die under the new treatment.
2. Determine the sample size required so that the estimate will be within 0.05 of the true proportion with 95% confidence.
3. Use 0.01 significance level to test the claim that the mortality rate has dropped.

Power is 1-0.7422=0.2578.

4. A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was know to protect the population for a mean of 36 months with a standard deviation of 3 months. To test the variability of the new shot, a r andom sample of 24 people was given the new shot. The regular blood tests showed that the sample standard deviation of protection time was 1.9 months.

1. At a 0.05 significance level, test the claim that the typhoid shot has a smaller variance of protection times.



The shot has a smaller variance of protection times.

2. Set up a 90% confidence interval for the population standard deviation.

4. A group of environmentalists claims that the warm water from Virginia Power plant at Lake Anna is limiting the growth of striped bass at the lake. In a similar southeastern reservoir the average weight of striped bass is 25 pounds with a sta ndard deviation of 8 pounds. A study of 30 striped bass at the Lake Anna revealed a mean weight of 20 pounds.

1. Do these data support the environmentalists? Use the 0.01 level of significance.



2. Set up a 90% confidence interval for the population mean weight of striped bass.

5. A biologist suspected that males age 20-24 have a higher mean systolic blood pressure than females in the same age group. Independent random samples of males and females were selected from the Framingham Heart Study. The data are as follows:

1. Give a 99% confidence interval for the mean difference in systolic blood pressure between the males and females.



2. At a 1% level of significance, is there sufficient evidence to justify the biologist's suspicion that males have a higher mean systolic blood pressure than females