Download Hypothesis Test 1 - Cabrillo College

In the following, state the null and alternative hypothesis (taken directly from text).
A new type of fertilizer is being tested on a plot of land in an orange grove to see if it
increases the amount of fruit production. The mean number of pounds of fruit on this plot of
land with old fertilizer was 400 pounds.
A sample of 100 flounder (a fish) of a certain species have a sample mean weight of 21.5
grams Scientist want to perform a hypothesis test to determine how strong the evidence is
that the mean weight differs from 20 grams.
A sample of 1004 adults will be conducted to see if they believe the federal government
should be limits on executive compensation. One highly paid executive claims that less than
50% of people believe that.
A marketing manager for a cell phone company claims that more than 35% of children aged
10-11 have cell phones. A survey of 5000 children will be conducted.
A new IQ test is created. The developer claims the population standard deviation is equal to
15. 25 people are tested.
Hypothesis Test 1
Quality Control. Pyrex makes measuring cups. A “one cup” measuring cup must be able to
measure a cup of liquid to within 2% of an actual cup. That is, a manufactured measuring cup
should measure 8 ounces plus or minus 2% (=+/- .16 ounces). Assume any errors from one cup are
distributed normally. A manufactured cup’s measurement has a mean of 8 ounces and a standard
deviation of .12 ounces. QC person will test 5 measuring cups and test their accuracy.
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Since the standard deviation is given, we will use which statistic?
We will use an alpha of 10%. What does this mean?
What is the value of the critical value?
Draw a bell curve to show the above.
The sample of the 5 cups has a sample mean of 8.08 ounces.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
Hypothesis Test 2
Cabrillo College is curious about how far the average person drives to the college. They wonder if
the average person drives less than 10 miles. We’re going to randomly sample 35 students to see.
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Since the standard deviation is NOT given, we will use which distribution?
We will use α=1%. What does this mean?
What is the critical value?
The sample shows a mean of 9.8 miles and a standard deviation of 5.4 miles.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
What would be a way to make this problem slightly more complicated while keeping it the
EXACT same problem?
Hypothesis Test 3, Proportion
It is believe that about 72% of the population thinks economists are useless to civilization. The
America Economic Association begins an advertising campaign to fight this. After the first month,
a survey of 200 people is conducted. 69% state that they believe economists are useless. Can we
conclude the campaign was effective?
State the null hypothesis:
State the alternative hypothesis:
Is this a one tail or two tail test? If one tail, which?
Do we know the standard deviation? Which distribution will we be using?
Let α = 5%. What does this mean?
What is the critical value?
Draw a bell curve to show the above.
What is the resulting test statistic?
What is the conclusion of the hypothesis test?
What is the p-value? What does that mean?
Homework: Section 9.2: #50, 53, 58 (2nd Ed: 52, 55, 60). Section 9.3: #16, 25 (2nd Ed 16, 27),
Section 9.4: #24, Section 9.5: #18
Note, we will also be doing section 13.1 on Hypothesis Testing with Regressions