MOD001021
2013/14
ANALYSIS OF BUSINESS
TUTORIAL 9
1. A consumer advocacy group suspects that a local supermarket’s 10-ounce packages of
cheddar cheese actually weight less than 10 ounces. The group took a random sample of 30
packages and found that the mean weight for the sample was 9.965 ounces. The population
follows a normal distribution with the population standard deviation of 0.15 ounce.
(a)State the null hypothesis and the alternative hypothesis.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
2. The manufacturer of a certain brand of auto batteries claims that the mean life of these
batteries is 45 months. A consumer protection agency that wants to check this claim took a
random sample of 30 such batteries and found that the mean life for this sample is 43.05
months. The lives of all such batteries have a normal distribution with the population standard
deviation of 6.5 months. Test the hypothesis with 95% of confidence level.
(a)State the null hypothesis and the alternative hypothesis in which the mean life of these
batteries is less than 45 months.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
3. A telephone company claims that the mean duration of all long-distance phone calls made by
its residential customers is 10 minutes. A random sample of 100 long-distance calls made by its
residential customers taken from the records of this company showed that the mean duration of
calls for this sample is 9.20 minutes. The population standard deviation is known to be 3.80
minutes.
Find the p-value for the test that the mean duration of all long-distance calls made by residential
customers is different from 10 minutes. If = 0.02, based on this p-value, would you reject the
null hypothesis? Explain. What if = 0.05?
1
4. A May 8, 2008, report on The Star noted that the average age of first-time mothers in the
Malaysia is slightly higher than 25 years. Suppose that a recently taken random sample of 57
first-time mothers from Pahang produced an average age of 23.90 years and that the population
standard deviation is known as 4.80 years.
Test the hypothesis using the p-value approach and ∝= 0.025.
(a)State the null hypothesis and the alternative hypothesis in which the average age of first-time
mother in Malaysia is less than 25 years.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
5. A production claims that an average of 50 boxes per hour are filled with finished goods at the
final stage of a production line. A random sampling of 48 different workers, at different times,
working at the end of identical production lines shows an average number of boxes filled as 51.5
with a standard deviation of 0.7 boxes. Does this evidence support the assertion by the
production manager at the 5% level of significance?
(a)State the null hypothesis and the alternative hypothesis.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
6. it is believed that the mean time that third year students spend in the library per week is 18
hours. Assume that the spent in the library is normally distributed. A random sample of 25
students gives mean time of 18.6 hours with a standard deviation of 1.02 hours. Test the view
that the mean time spent in the library is greater than 18 hours at th 5% significance level.
(a)State the null hypothesis and the alternative hypothesis.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
2
7. suppose we want to test of a random sample of eight cartons, whether the average fat
content of a certain make of ice cream is less than 15%. The sample mean for fat content is
found to be 14.3% with a sample standard deviation of 0.96%. what conclusion would you come
to at 1% significance level?
(a)State the null hypothesis and the alternative hypothesis.
(b) Is it a two-tailed test, right-tailed test or left-tailed test?
(c) Calculate the α.
(d) Calculate the p-value.
(e) Would you accept or reject the null hypothesis? State the reason.
8. Using the following observations recorded by a researcher, check if the assumption of no
relation between lung cancer and smoking can be accepted at 5 % level of significance.
Cancer suffers
Non sufferers
Total
Smoker
200
150
350
Non-smoker
200
450
650
3
Total
400
600
1000