Question

For each claim, state H0 and Ha. Then determine whether the hypothesis test is a left-

tailed, right-tailed, or two-tailed test
Example 1:
A manufacturer claims that its rechargeable batteries have an average life of at least 1,000
charges.
H0 :
HA :
Example 2:
Statesville college claims that 94% of their graduates find employment within six months of
graduation.
H0:
HA:
Example 3:
A local telephone company claims that the average length of a phone call is 8 minutes.
H0 :
HA :
Example 4:
A cigarette manufacturer claims that less than one-eighth of the US adult population smokes
cigarettes.
H0:
HA:
Example 5:
An engineer measured the hardness of 25 pieces of ductile iron. The engineer hypothesized that
the mean hardness of all such ductile iron pieces is greater than 170.
Therefore, he was interested in testing the hypotheses:
H0 :
HA :
Example 6:
A biologist was interested in determining whether sunflower seedlings treated with an extract
resulted in a lower average height of sunflower seedlings than the standard height of 15.7 cm. The
biologist treated a random sample of n = 33 seedlings with the extract and subsequently obtained
their heights.
The biologist's hypotheses are:
H0 :
HA :
Example 7:
A manufacturer claims that the thickness of the spearmint gum it produces is 7.5 one-hundredths
of an inch. A quality control specialist regularly checks this claim. On one production run, he took
a random sample of n = 10 pieces of gum and measured their thickness.
The quality control specialist's hypotheses are:
H0 :
HA :
Example 8:
Consider the population of many adults. A researcher hypothesized that the average adult body
temperature is lower than the often-advertised 98.6 degrees F. That is, the researcher wants an
answer to the question: "Is the average adult body temperature 98.6 degrees? Or is it lower?" To
answer his research question, the researcher starts by assuming that the average adult body
temperature was 98.6 degrees F.
Then, the researcher went out and tried to find evidence that refutes his initial assumption. In
doing so, he selects a random sample of 130 adults. The average body temperature of the 130
sampled adults is 98.25 degrees.
H0 :
HA :
Example 9:
Newborn babies are more likely to be boys than girls. A random sample found 13,173 boys were
born among 25,468 newborn children. The sample proportion of boys was 0.5172. Is this sample
evidence that the birth of boys is more common than the birth of girls in the entire population?
Here, we want to test
H0:
HA:
Steps in Hypothesis Testing (these steps include materials from Chapter 13):
1. Step 1: State Hypotheses
2. Step 2: Select alpha, Draw Picture, Label Critical Values and Rejection Region(s)
3. Step 3: Select Test Statistic
4. Step 4: State Decision Rule
5. Step 5: Calculate Test Statistic (Ch13) or P-value, Make Decision
6. Step 6: Take Action; State what the results mean
Example 1: According to a website, the average price charged to a customer to have a 12 by 18
wall-to-wall carpet shampoo cleaning is about $50. Suppose that a start-up company believes that
in the region that they operate, the average price is higher. To test this hypothesis, the company
randomly contacts 23 customers who have recently had a 12 by 18 wall-to-wall carpet shampoo
cleaning and asked the customers how much they were charged for the job. Suppose the resulting
data are given below and that the population standard deviation price is $3.49. Use a 10% level of
significance to test their hypothesis.
x= $52.17 n = 23 σ= $3.49 a = .10
Example 2: Suppose that in the past years the average price per square foot for warehouses in
the U.S. has been $32.28. A national real estate investor wants to determine whether the figure
has changed now. The investor hires a researcher who randomly samples 49 warehouses that are
for sale across the U.S. and finds that the mean price per square foot is $31.67, with a standard
deviation of $1.29. Assume that the prices of warehouses footage are normally distributed in the
population. If the researcher uses a 1% level of significance, what statistical conclusion can be
reached?
Example 3: A large manufacturing company investigated the service it received from suppliers
and discovered that, in the past, 32% of all materials shipments were received late. However, the
company recently installed a just-in-time system in which suppliers are linked more closely to the
manufacturing process. A random sample of 118 deliveries since the just-in-time system was
installed reveals that 22 deliveries were late. Use this sample information to test whether the
proportion of late deliveries was reduced significantly. Let α=.05.

Answer 1

1. H: Average life of rechargeable batteries ≥ 1,000 charges.

Hg: Average life of rechargeable batteries < 1,000 charges.

Test: Left-tailed test.

2. H: Proportion of graduates finding employment within six months = 94%.

Hg: Proportion of graduates finding employment within six months ≠ 94%.

Test: Two-tailed test.

3. H: Average length of a phone call = 8 minutes.

Hg: Average length of a phone call ≠ 8 minutes.

Test: Two-tailed test.

4. H: Proportion of US adult population smoking cigarettes < 1/8.

Hg: Proportion of US adult population smoking cigarettes ≥ 1/8.

Test: Left-tailed test.

5. H: Mean hardness of ductile iron pieces > 170.

Hg: Mean hardness of ductile iron pieces ≤ 170.

Test: Right-tailed test.

6. H: Average height of treated sunflower seedlings < 15.7 cm.

Hg: Average height of treated sunflower seedlings ≥ 15.7 cm.

Test: Left-tailed test.

7. H: Thickness of spearmint gum produced = 7.5 one-hundredths of an inch.

Hg: Thickness of spearmint gum produced ≠ 7.5 one-hundredths of an inch.

Test: Two-tailed test.

8. H: Average adult body temperature = 98.6 degrees F.

Hg: Average adult body temperature < 98.6 degrees F.

Test: Left-tailed test.

9. H: Proportion of boys born > proportion of girls born.

Hg: Proportion of boys born ≤ proportion of girls born.

Test: Right-tailed test.

For each example, H represents the null hypothesis and Hg represents the alternative hypothesis. The null hypothesis assumes a specific value or relationship, while the alternative hypothesis suggests a different value or relationship.

The type of hypothesis test (left-tailed, right-tailed, or two-tailed) depends on the directionality of the alternative hypothesis. In a left-tailed test, the alternative hypothesis suggests a smaller value. In a right-tailed test, the alternative hypothesis suggests a larger value. In a two-tailed test, the alternative hypothesis suggests a difference in either direction.

In the provided examples, the type of test is determined based on the wording of the alternative hypothesis. If the alternative hypothesis specifies a direction (e.g., "greater than" or "less than"), it corresponds to a one-tailed test. If the alternative hypothesis simply states a difference (e.g., "not equal to"), it corresponds to a two-tailed test.

It is important to correctly identify the type of test to determine the critical region and interpret the test results accurately.