1. Ten successively tested light bulbs functioned for the
following lengths of time (measured in hours):
36, 39, 18, 42 45, 35, 28, 24, 20, 40 Assuming that the measurements represent is a random
sample from a normal population.
?a. Given that =10, find a 95% confidence interval
estimate of the mean life of a light bulb.
b. Give a 90% confidence interval estimate of the mean
life of a light bulb.
c. A claim has been made that the results of this
experiment indicate, “One can be 90% confident that
the true mean life exceeds 30 hours.” Do you agree
with this statement? Explain. Note use your results in
2. The weight of salmon grown at a commercial hatchery
has a standard deviation of 1.2 pounds. The hatchery
claims that the mean weight is at least 7.6 pounds. A
random sample of 36 fish yielded and average weight of
8.2 pounds and 1.5 pounds as a standard deviation.
a. Is there is strong evidence to reject the hatchery’s
claims at the 1% level of significance? Use the p-value
method to test the hatchery’s claims.
b. Estimate the population mean of the salmon using
95% confidence level. And interpret your results.
3. Out of a random sample of 120 students at a
university, 12 stated that they were smokers.
a. Construct a 98% confidence interval estimate of the
true proportion of all the students at the university
who are smokers.
b. How large a sample is needed to ensure that the
length of the 95% interval estimate of the true
proportion is within ??0.03? c. Test the claim that that the true proportion of
nonsmokers is less than 13%, use 1% level of
4. A high school is interested in determining whether two
of its instructors are equally able to prepare students for
countrywide examination in Statistics. Seventy two
students taking Statistics this semester were randomly
divided into tow groups of 36 each. Instructor 1 taught
Statistics to the first group, and instructor 2 to the
second group. At the end of semester, the students took
the countrywide examination, we get the following
Class 1 70.6 81.6
Class 2 74.2 36.2 Can you conclude from these results that the
instructors are not equally able in preparing students
for the examination? Use 5% and 1% level of
significances. Give the null and alternative hypotheses
and the resulting of the p-value. What are your final
5. A taxi company is trying to decide whether to purchase
brand A or brand B tires for its fleet of taxis. To
estimate the difference in the two brands, an experiment
is conducted using a sample of 10 tires of each brand.
The tires are run until they wear out. The results are
Mean in K Standard deviation in K
Brand A 36,500 5,000
Brand B 39,300 7,100
Assume that the variances are equal.
a. Compute a 95% confidence interval for the
difference between the two population means.
What is your interpretation of your finding?
b. Use 5% level of significant to test the null
hypothesis that there is no difference between the
c. What are the assumptions that you need to answer
the above two questions.
d. What is your final conclusion about the difference
between the two brands of tires?