Statistics: Complement of a claim;
P value; critical z value
1. Use
the given statement to represent a claim. Write its complement and state which
Ho and which H a.
? ? 406
Find the complement of the claim.
2. Find
the P-value for the indicated hypothesis test with the given standardized test
statistic, z. Decide whether to reject Ho for the give level of significance a.
Two-tailed test with test statistic z= -2.23 and a=0.05. P-value = ? Round to
four decimal places as needed.
3. Find
the critical z values. Assume that the normal distribution applies.
Right-tailed test; a=0.01. Z=? Round to two decimal places as needed.
4. Find
the critical value(s) for the left-tailed test with a=0.05. Include a graph
with your answer. The critical value (s) is (are)?
5. A
company that makes cola drinks states that the mean caffeine content per 12-
ounce bottle of cola is 40 milligrams. You want to test this claim. During your
tests, you find that a random sample of thirty 12-ounce bottles of cola has a
mean caffeine content of 37.7 milligrams with a standard deviation of 7.1
milligrams. At a= 0.02, can you reject the company’s claim? Complete part (a)
through (e).
(a) Identity
Ho and Ha. Choose the correct answer below.
6. A
light bulb manufacturer guarantees that the mean life of a certain type of
light bulb is at least 700 hours. A random sample of 49 lights bulbs has a mean
life of 683 hours with a standard deviation of 80 hours. Do you have enough
evidence to reject the manufacturer’s claim? Use a=0.04
(A) Identify
the null hypothesis and alternative hypothesis
7. An
environmentalist estimates that the mean waste recycled by adults in the
country is more than 1 pound per person per day. You want the test this claim.
You find that the mean waste recycled per person per day for the random sample
of 11 adults in the country is 1.2 pounds and the standard deviation is 0.4
pound. At a= 0.10, can you support the claim? Assume the population is normally
distributed.
(A) Write the
claim mathematically and identify Ho and Ha. How to correctly state Ho and Ha?
8. A
country is considering raising the speed limit on a road because they claim
that the mean speed of vehicles is greater than 30 miles per hour. A random
sample of 15 vehicles has a mean speed of 34 miles per hour and a standard
deviation of 4.7 miles per hour. At a=0.01, do you have enough evidence to
support the country’s claim? Completed parts (a) through (d).
Write the claim mathematically and
identify Ho and Ha.
9. A
travel association claims that the mean daily meal cost for two adults
traveling together on vacation is $100. A random sample of 15 such groups of
adults has a mean daily meal cost of $105 and standard deviation of $ 7.50. Is
there enough evidence to reject the claim at a= 0.05? Complete parts (a)
through (d) below. Write the claim mathematically and identify Ho and Ha.
10. (a) Write
the claim mathematically and identify Ho and Ha. (b) Find the critical value
(s) and identify the rejection region(s). (c) Find the standardized test
statistic. (d) Decide whether to reject or fail to reject the null hypothesis.
An environmental agency recently claimed more than 32% of consumers have
stopped buying a certain product because of environmental concerns. In a random
sample of 1050 consumers, you find 36% have stopped buying the product. At
a=0.03, do you have enough evidence to support the claim? How would you
correctly state Ho and Ha?
11. A humane
society claims that less than 38% of U.S. households own a dog. In a random
sample of 408 U.S. households, 156 say they own a dog. At a= 0.04, is there
enough evidence to support the society’s claim? (a) Write the claim
mathematically and identify Ho and Ha. (b) Find the critical value (s) and
identify the rejection region (s). (c) Find the standardized test statistic.
(d) Decide whether to reject or fail to reject the null hypothesis, and (e)
interpret the decision in the context of the original claim.
(a) How would
you correctly state Ho and Ha?
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