Building confidence intervals for proportions

Textbook- BSTAT2 Keller

Chapter 9- Introduction to Estimation and Chapter 10 introduction to Hypothesis Testing

9.1 In a random sampleof 500 observations , we found the proportion of successes to be 48%. Estimate with 95% confidence the population proportion of successes.
b. Repeat part (a) with n=200
c. repeat part (a) with n = 1000
d. Describe the effect on the confidence intervalestimate of increasing the sample size

9.3 A statisticspractitioner working for Major League Baseball wants to supply radio and television commentators with interesting statistics. He observed several hundreds fames and counted the number of times a runner on first base attempted to steal second base. He found there were 373 such events, of which 259 were successful. Estimate with 95% confidence the proportion of all attempted thefts of second base that are successful.

Chapter 10 –

It is the responsibility of the federal government to judge the safety and effectiveness of new drugs. There are two possible decisions: approve the drug or disapprove the drug.

10.3 You are pilot of a jumbo jet. You smell smoke in the cockpit. The nearest airport is less than 5 minutes away. Should you land the plane immediately?

10.5
a. calculate the p-value of the test of the following hypotheses given that p=.63 and n=100:
Ho: p =.60 H1: p>.60
b. repeat part (a) with n =200 c. repeat part (a) with n =400 D. Describe the effect the P-value of increasing the sample size.

9.1 a. At 95% level, the critical value is 1.96 using normal distribution table, so a 95% confidence interval=[0.48-1.96*sqrt(0.48*0.52/500), 0.48+1.96*sqrt(0.48*0.52/500)]=[0.4786, 0.4814]

b. When n=200, a 95% confidence interval=[0.48-1.96*sqrt(0.48*0.52/200), 0.48+1.96*sqrt(0.48*0.52/200)]=[0.4765, 0.4835]

c. When n=1000, a 95% confidence …

The solution gives detailed steps on solving several questions on building confidence intervals for proportions and calculating p-values using normal distributions.