Hypothesis Testing

Problem 10.17

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.

Answer)

Problem 10.18

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.

Answer)

Problem 10.20

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.

Answer)

b) Test your hypotheses using a = 0.05.

Answer)

c) Find the p value.

Answer)

d) Based on the p value, what can you conclude about the average length
of life for patients who receive the vaccine?

Answer)

Problem 10.22

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.

Answer)

b) Test your hypotheses using a = 0.05

Answer)

c) Find the p value.

Answer)

d) Based on the p value, should the tennis pro invest in the new racket?

Answer)