Discuss the below in detail:
Q1 M&M/Mars claims that at least 20% of the M&M's in each package are the new blue color. Set up the null and alternate hypotheses to test this claim.
Q2 The computer center at a university claims that the average amount of time that students spend on-line has increased from last year's average of 1 hour per day. Set up the null and alternative hypotheses to test this claim.
Q3 Recent medical research indicates that skin caner patients who receive a new medication for skin cancer live longer than those who do not. The average length of life prior to the development of this medication was 18 months. The medical community wishes to test the claim made by the developers of this drug. A sample of 35 patients who received the medication lived an average of 21 months. Te standard deviation is 5 months.
a) Set up the null and the alternative hypotheses to test if average length of life has increased from 18 months.
b) Test your hypotheses using a = 0.05.
c) Find the p value.
d) Based on the p value, what can you conclude about the average length of life for patients who receive the vaccine?
Q4 A manufacturer of top-of-line tennis rackets claims that its Smack Em tennis racket will change a player's game. A tennis pro currently serves the ball at an average speed of 115 mph with a standard deviation of 2.5 mph. The speeds are normally distributed. The tennis pro decides to test the company's claim and records the speed of his serve for 15 balls using the Smack Em racket. The data are shown in the following table: Speed
117.3 115.9
115.1 115.2
116.0 115.0
116.2 113.0
112.9 120.8
115.4 116.9
113.8 114.4
114.2
a) Set up the null and the alternative hypotheses to test if the average service speed has increased using the new racket.
b) Test your hypotheses using a = 0.05
c) Find the p value.
d) Based on the p value, should the tennis pro invest in the new racket?