I have statistics question need to be solved

Fix the errors

8. What percentage of your campus student body is female? Let p be the proportion of women students on your campus.

(a) If no preliminary study is made to estimate p, how large a sample is needed to be 99% sure that a point estimate p̂ will be within a distance of 0.050 from p? 
  
(b) A report indicates that approximately 54% of college students are females. Answer part (a) using this estimate for p. 
 

9. The National Council of Small Businesses is interested in the proportion of small businesses that declared Chapter 11 bankruptcy last year. Since there are so many small businesses, the National Council intends to estimate the proportion from a random sample. Let p be the proportion of small businesses that declared Chapter 11 bankruptcy last year.

(b) In a preliminary random sample of 30 small businesses, it was found that twelve had declared Chapter 11 bankruptcy. How many more small businesses should then be included in a sample to be 99% sure that a point estimate p̂ will be within a distance of 0.088 from p? 
 

17. A study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x1 be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x2 be the empathy score of a father. A random sample of 38 mothers gave a sample mean of x1 = 69.04. Another random sample of 28 fathers gave x2 = 61.38. Assume that σ1 = 11.06 and σ2 = 12.32.

(a) Let μ1 be the population mean of x1 and let μ2 be the population mean of x2. Find a 95% confidence interval for μ1 – μ2. (Use 2 decimal places.)

35. How effective is gastric bypass surgery in maintaining weight loss in extremely obese people? A study conducted found that 71% of a sample of 419 subjects who had received gastric bypass surgery maintained at least a 20% weight loss six years after surgery.

(a) Are the conditions for the use of the large sample confidence interval met?

YesNo    

(b) Give a 90% confidence interval for the proportion of those receiving gastric bypass surgery that maintained at least a 20% weight loss six years after surgery. (Round your answers to four decimal places.)
 to  
(c) Interpret your interval in the context of the problem. (Round your answers to two decimal places.)

Based on this study, we estimate with 90% confidence that between  % and % of all gastric bypass patients will maintain at least a 20% weight loss for six years after surgery.

44. A study of the effect of exposure to color (red or blue) on the ability to solve puzzles used 42 subjects. Half the subjects (21) were asked to solve a series of puzzles while in a red-colored environment. The other half were asked to solve the same series of puzzles while in a blue-colored environment. The time taken to solve the puzzles was recorded for each subject. To compare the mean times for the two groups of subjects using statistical procedures, what is the degrees of freedom? 
d.f.  

48. Independent random samples of professional football and basketball players gave the following information. Assume that the weight distributions are mound-shaped and symmetric.

Weights (in lb) of pro football players: x1; n1 = 21

Weights (in lb) of pro basketball players: x2; n2 = 19

(b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to one decimal place.)