Please help with statistics hw questions. Thank you for your time

3. Leroy, a starting player for a major college basketball team, made only 38.4% of his free (I point) throws last season. During the summer he worked on developing a softer shot in the hope of improving his free-throw accuracy. In the rst eight games of this season Leroy made 25 free throws in 40 attempts. Let p be his probability of making each free throw he shoots this season. a. State the null hypothesis H0 that Leroy's free-throw probability has remained the same as last year and the alternative Ha that his work in the summer resulted in a higher probability of success. b. Calculate the 2 statistic for testing H0 versus Ha. c. Do you accept or reject H0 for a = 0.05? Find the P-value. d. Give a 90% condence interval for Leroy's free-throw success probability for the new season. Are you convinced that he is now a better free-throw shooter than last season? e. What assumptions are needed for the validity of the test and condence interval calculations that you performed? 4. A software company is planning for an upgrade of its software. You must charge customers $100. Are your customers willing to pay this much? You contact a random sample of 40 customers and nd that 11 would pay $ 100 for the upgrade. If the upgrade is to be protable, you will need to sell it to more than 20% of your customers. Do the sample data give good evidence that more than 20% are willing to buy? a. Formulate this problem as a hypothesis test. Give the null and alternative hypotheses. b. Carry out the signicance test. Report the test statistic and the P-value. 0. Should you proceed with plans to produce and market the upgrade? (I point) 1 . Part 1 : What are the conditions for using the standard deviation formula when conducting a ( 1 point ) significance test ? Be specific about p versus p-hat . Part 2 : What are the conditions for approximative with a normal distribution ?"2 . In each of the following cases state whether or not the normal approximation to the binomial ( 1 point ) should be used for a significance test on the population proportion p . 2 . 7 = 10 and Ho : 1 - 0. 4. b. 1 = 100 and Ho : p = 0. 6. C . 1 = 1, 000 and Ho : p = 0. 996. d . n = 500 and Ho : P = 0. 3