Efficacy of a drug | Mathematics homework help

1. Efficacy of a drug. Seventy-five (75) people with hypertension were given a new drug for the treatment of their condition. Blood pressure was lowered sufficiently to reduce the risk of serious outcomes in 20 of the 75 patients.
(A) In what proportion of the sample did the drug work? (Calculate P).(2 points)
(B) Calculate a 95% confidence interval for the proportion. Show all work, and interpret your findings. (Check to see if you can use a normal approximation before calculating the confidence interval.) (4 points)
(C) How large a sample would be needed to reduce the margin of error to .05? (4 points)
2. Determine the sample size needed to calculate a 95% confidence interval for a proportion with a margin or error of 10%. (4 points)
3. Survival in pediatric cancer cases. An oncologist treats 40 cases of kidney cancer. In the past, this disease had a five-year survival rate of 1 in 5 (20%). In the 40 patients the oncologist treats, 16 survive for at least five years. Test to see whether this treatment is associated with a significantly higher survival than in the past. (Let a = .01, two-sided.) List all hypothesis testing steps. Was survival improved significantly? (8 points)
4. Cancers in insulation workers. There were 26 cancer deaths in a cohort of 556 insulation workers. Based on studies in comparably populations, only 14.4 cancer deaths were expected.
(A) What was the observed cancer morality proportion in the group?(2 points)
(B) What was the expected cancer mortality proportion in the group under H0? (2 points)
(C) Test whether the observed mortality proportion is significantly greater than expected. Use a two-sided test at a = .01 level. List all hypothesis testing steps (including H0 and Ha), and show all work. (8 points)

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A teacher asked her 8 introductory stat students to record the total amount of time they spent studying for a test. The amounts of time x (in hours) and the resulting test grades y are given below:

X: 2 1 1.5 0.5 1 3 0 2
Y: 92 81 84 68 85 96 48 74

make a scatterplot of the data.
use your ti-83 to obtain the equation of the least squares regression line and the correlation.
explain in words what the slope B of the true regression line says about hours studied and grade awarded.
What is the estimate of B from the data? What is your estimate of the intercept a of the true regression line?
Use your calculator to calculate the residuals. Report the sum of the residuals and the sum of the squares of the residuals. Then use these results to estimate the standard deviation sigma in the regression model.
The standard error of the slope SEb is defined as Calculate SEb
Suppose we want to find out if the number of hours studied helps predict grade awarded on this statistics test. formulate null and alternative hypotheses about the slope of the true regression line. state a two sided alternative
Determine the test statistic, the degrees of freedom and the P value of t against the alternative.
Would you reject the null hypothesis at the 1% signifance level? Explain briefly.
Write your conclusion in plain language
Compute a 95% confidence interval for the slop B of the true regression line.                 

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