Question

Q1) Suppose a production line operates with a mean filling weight of 16 ounces per container. Since
over- or under-filling can be dangerous, a quality control inspector samples of 24 items to determine
whether the filling weight must be adjusted. The sample revealed a mean of 16.32 ounces with a
sample standard deviation of 0.8 ounces. Using a 0.10 level of significance, can it be concluded that the
process is out of control (not equal to 16 ounces)?
Q2) A survey done one year ago showed that 45% of the population participated in recycling programs.
In a recent poll a random sample of 1250 people showed that 598 participate in recycling programs. Test
the hypothesis that the proportion of the population who participate in recycling programs is greater
than it was one year ago. Use a 5% significance level.
Q3) Marla is studying the sodium content of cold cuts. A random sample of 8 52-gm samples of smoked
beef produced sample mean 14.04 gm of sodium with sample standard deviation 0.50 gm. An
independent random sample of 6 52-gm samples of smoked turkey produced sample mean 13.52 gm
sodium with sample standard deviation 0.75 gm. Test the claim that there is a difference in the mean
sodium content of the above brands of smoked ham and smoked turkey. Use a 5% significance level.
Assume that population variances are not equal.
Q4) A pilot study in Fair weather County wishes to determine whether mailing reminders to register to
vote to all citizens in the county who are eligible will improve voter registration numbers. A random
sample of 1500 potential voters was taken. Then this sample was randomly divided into two groups.
Group 1 consisted of 750 people. Reminders were sent in the mail to each member in the group. The
number from this group who registered was 405.
Group 2 consisted of 750 people. No reminders to register were sent to them. The number of potential
voters from this group who registered was 375.
Let 1p be the proportion of voters who registered in group 1, and let p2 be the proportion registered
from group 2.
Test using a 5% level of significance to see whether the claim that the proportion of potential voters
who registered was greater in group 2.

Answer 1

Given:

Sample size, n = 24

Sample mean, = 16.32

sample standard deviation, s = 0.8

Significance level, = 0.10

Therefore there is sufficient evidence to concluded that the process is out of control at 0.10 evel of significance.