Statistics- Use the given statement to represent a claim

1.
Determine whether the statement is
true or false. If it is false, rewrite it as a true statement.
In a hypothesis test, you assume the
alternative hypothesis is true.

2.
Use the given statement to represent a
claim. Write its complement and state which H0
and which is Ha.
μ ≤ 565

3.
Use the given statement to represent a
claim. Write its complement and state which is H0 and which is Ha.
σ ≠ 4

4.
A null and alternative hypothesis are
given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.
H0:
σ ≥ 8.9
Ha: σ
≥ 8.9

5.
Write the null and alternative
hypothesis. Identify which is the claim.
A light bulb manufacturer claims that
the mean life of a certain type of bulb is less than 800 hours.

6.
A local chess club claims that the
length of time to play a game has a standard deviation of more than 15 minutes.
Write sentences describing type I and type II errors for a hypothesis test of
this claim.

7.
A film developer claims that the mean
number of pictures developed for a camera with 24 exposures is less than 23. If
a hypothesis test is performed, how should you interpret a decision that (a)
rejects the null hypothesis and (b) fails to reject the null hypothesis?

8.
Your medical research team is
investigating the mean cost of a 30-day supply of a certain heart medication. A
pharmaceutical company thinks that the mean cost is more than $71. You want to
support this claim. How would you write the null and alternative hypothesis?
9.
The three confidence intervals to the
right represent three samplings. Decide whether each confidence interval
indicates that you should reject H0.
Explain your reasoning.
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10.
Find the P-value for the indicated hypothesis test with the given
standardized test statistic, z.
Decide whether to reject H0
for the given level of significance α
= 0.05

11.
Match each P-value with the graph that correctly displays its area
P = 0.2611
P = 0.0614
P
= 0.0307 P = 0.1492
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12.
Find the critical z values. Assume that the normal distribution applies.
Right-tailed
test; α = 0.10

13.
State whether the standardized test
statistic z indicates that you should
reject the null hypothesis.
a.
z
= 1.211
b.
z
= 1.305
c.
z
= –1.113
d.
z
= –1.497

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14.
A random sample of 78 eight grade
students’ scores on a national mathematics assessment test has a mean score of
263 with a standard deviation of 30. This test result prompts a state school
administrator to declare that the mean score for the state’s eighth graders on
this exam is more than 260. At α =
0.08, is there enough evidence to support the administrator’s claim? Complete
parts (a) through (e).
a.
Write the claim mathematically and
identify H0 and Ha.
b.
Find the standardized test statistic z, and its corresponding area.
c.
Find the P-value
d.
Decide whether to reject or fail to
reject the null hypothesis.
e.
Interpret your decision in the context
of the original claim.

15.
A scientist estimates that the mean
nitrogen dioxide level in a city is greater than 29 parts per billion. To test
this estimate, you determine the nitrogen dioxide levels for 31 randomly
selected days. The results (in parts per billion) are listed to the right. At α = 0.03, can you support the
scientist’s estimate? Complete parts (a) through (e).
a.
Find the critical value and identify
the rejection region.
b.
Find the standardized test statistic.
c.
Decide whether to reject or fail to
reject the null hypothesis.
d.
Interpret the decision in the context
of the original claim.

16.
You believe that the mean annual
kilowatt hour usage of residential customers in a certain region is less than
13,500. You find that a random sample of 33 residential customers has a mean
kilowatt hour usage of 13,300 with a standard deviation of 310 kilowatt hours.
You conduct a statistical experiment where H0: μ ≥ 13,500 and Ha:
μ < 13,500. At α = 0.01, decide whether to reject or fail to reject the null hypothesis. a. Find the critical value(s). b. Find the standardized test statistic. c. State your conclusion. 17. Find the critical value(s) for the indicated t-test, level of significance α, and sample size n. Left-tailed test, α = 0.01, n = 17 Area under the curve for the t-distribution. .0/msohtmlclip1/01/clip_image005.gif">

18.
State whether the standardized test
statistic t indicates that you should reject the null hypothesis. Explain.
a.
t
= 1.875
b.
t
= 0
c.
t
= –1.742
d.
t
= –1.911
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19.
An environmentalist estimates that the
mean waste recycled by adults in the country is more than 1 pound per person per
day. You want to test this claim. You find that the mean waste recycled per
person per day for a random sample of 11 adults in a country is 1.8 pounds and
the standard deviation is 0.2 pound. At α
= 0.05, can you support the claim? Assume the population is normally
distributed.
a.
Which of the following correctly
states H0 and Ha?

A. H0:
μ = 1
Ha: μ > 1

B. H0:
μ = 1
Ha:
μ ≠ 1

C. H0:
μ ≥ 1
Ha:
μ < 1 D. H0: μ > 1
Ha:
μ ≤ 1

E. H0:
μ = 1
Ha:
μ < 1 F. H0: μ ≤ 1 Ha: μ > 1

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.
e.
Interpret the decision in the context
of the original claim.

20.
For your study on the food consumption
habits of teenage males, you randomly select 10 teenage males and ask each how
many 12-ounce servings of soda he drinks each day. The results are listed
below. At α = 0.01, is there enough
evidence to support the claim that teenage males drink fewer than three
12-ounce servings of soda per day? Assume the population is normally
distributed.
3.4
2.2 2.5 2.8
1.9 2.3 2.9
3.1 3.8 1.3
a.
Write the claim mathematically and
identify H0 and Ha.
b.
Use technology to find the P-value.
c.
Decide whether to reject or fail to
reject the null hypothesis.
d.
Interpret the decision in the context
of the original claim.

21.
Decide whether the normal sampling
distribution can be used, test the claim about the population proportion p at the given level of significance α using the given sample statistics.
Claim:
p ≠ 0.26; α = 0.10; Sample statistics:.0/msohtmlclip1/01/clip_image008.gif”>= 0.21, n = 200
a.
State the null and alternative
hypotheses.
b.
Determine the critical value(s).
c.
Find the z-test statistic
d.
What is the result of the test?

22.
A medical researcher says that at
least 27% of adults are smokers. In a random sample of 200 adults, 22.5% say
they are smokers. At α= 0.03, do you
have enough evidence to reject the researcher’s claim?
a.
Write the claim mathematically and
identify H0 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.

23.
In a sample of 1784 home buyers, you
find that 823 home buyers found their real estate agents through a friend. At α = 0.02, can you reject the claim that
50% of home buyers find their real estate agent through a friend?
a.
Write the claim mathematically and
identify H0 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.

24.
State whether the standardized test
statistic X2 allows you to
reject the null hypothesis.
X2 = 18.301
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25.
Use a 0.05 significance level to test
the claim that peanut candies have weights that vary more than plain candies.
The standard deviation for the weights of plain candies is 0.261. A sample of
61 peanut candies has weights with a standard deviation of 0.36. Assume the
population is normally distributed.
a.
Write the claim mathematically and identify
H0 and Ha.
b.
Find the critical value(s).Identify
the rejection region(s).
c.
Use the X2-test to find the standardized test statistic.
d.
Decide whether to reject or fail to
reject the null hypothesis.
e.
Interpret the decision in the context
of the original claim.
Does it appear that peanut candies have
weights that vary more than those of plain candies?