Name: ______________________________________
CHS Stat Chi Square Distribution
1)
In 1941, the population standard deviation for the age of a rural Quebec woman at the time of her first
marriage was 2.3. Suppose a recent study of age at first marriage for a random sample of 41 women in rural
Quebec gave a sample standard deviation of 1.8. Use a 5% significant level to test the claim that the current
standard deviation is less than 2.3.
2)
Jim Mead is a veterinarian who visits a Vermont farm to examine prize bulls. In order to examine a bull, Jim first
gives the animal a tranquilizer shop. The effect of the shot is supposed to last an average of 65 minutes, and it
usually does. However, Jim sometimes gets chased out of the pasture by a bull that recovers too soon, and
other times he becomes worried about prize bulls that take too long to recover. By reading journals, Jim has
found that the tranquilizer should have a mean duration time of 65 minutes, with a standard deviation of 15
minutes. A random sample of 10 of Jim’s bulls had a mean tranquilized duration time of close to 65 minutes but
a standard deviation of 24 minutes. At a 1% significance level, test Jim’s claim that the standard deviation is
larger than stated in his journal.
3) The fan blades on commercial jet engines must be replaced when wear on these parts indicates too much
variability to pass inspection. If a single fan blade broke during operation, it could severely endanger a flight. A
large engine contains thousands of fan blades, and safety regulations require that standard deviation of all
blades not exceed 0.42. An engine inspector took a random sample of 61 fan blades from an engine. She
measured each blade and found a sample standard deviation of 0.52. Using a 0.01 significance level, test the
claim that all the engine fan blades must be replaced.
4)
A new kind of typhoid shot is being developed by a medical research team. The old typhoid shot was known to
protect the population with a standard deviation of 3 months. To test the standard deviation of the new shot, a
random sample of 23 people were given the new shot. Regular blood tests showed that the sample standard
deviation protection was 1.9 months. Using a 0.05 significance level, test the claim that the new typhoid shot
has a standard deviation of 3 months.