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In a clinical study of an allergy drug, 108 of the 203 subjects
reported experiencing significant relief from their symptoms. Using a
significance level of .01, test the claim that more than half of all
those using the drug experienced relief.
According to a recent poll, 53% of Americans would vote for an incumbent
president. If a sample of 100 people results in 45% who would vote for
the incumbent, test the claim that the percentage is 53%. Use a .10
3. A public bus company official claims that the
mean waiting time for bus number 14 during peak hours is less than 10
minutes. Karen took bus 14 during peak hours on 18 different occasions.
Her mean waiting time was
7.4 minutes. Assume that the standard deviation has been historically
known to be 2.2 minutes. At the .05 significance level, test the claim that the mean waiting time is less than 10 minutes.
4. The world’s smallest mammal is the bumblebee bat. Such bats are roughly
the same size of a large bumblebee. Listed below are the weights (in
grams) from a sample of these bats. Assuming that all such bats have a
standard deviation of .3 grams, use a significance level of .05 to test the
claim that these bats are from the same population with a known mean of
grams. Do the bats appear to be from the same population ? You may
assume the sample data comes from a population that follows a normal
2.13 1.31 1.91 1.92 1.77 1.64 2.29 1.99 2.33 2.49 2.22
A manufacturer makes steel rods that are supposed to have a mean length
of 50 centimeters. A retailer suspects that the bars are being produced
too short. A sample of 46 bars is taken and their mean length is
determined to be 51 centimeters with a standard deviation of 3.6
centimeters. Using a .01 significance level, test the retailers claim
that the population mean is less than 50 centimeters.
6. A cereal
company claims that the mean weight of the cereal in its packets is more
than 14 oz. The weights (in ounces) of the cereal in a random sample of
8 cereal packets are listed below. You may assume the sample data comes
from a population that follows a normal distribution. Using a
.05 level of significance test the company’s claim.
14.6 13.8 14.1 13.7 14.0 14.4 13.6 14.2
An article in a journal reports that 34% of American fathers take no
responsibility for child care. A researcher claims that the figure is
higher for fathers in the town of Littleton. A random sample of 225
fathers from Littleton, yielded 97 who did not help with child care.
Using a .05 level of significance test the claim that the proportion is
at least 34%.
8. The average time it takes for a person to experience relief from aspirin is
minutes. A new ingredient is added to help speed up relief. A study was
conducted with 35 people that resulted in a mean of 22.1 minutes with a
standard deviation of 1.9 minutes. Using a .05 significance level, test
claim that the mean amount of time relief will be felt is less than 25 minutes.
A Patent Medicine Company supervisor assumes that the bottling machine
is operating properly if only 5 percent of the processed bottles are not
full. A random sample of 100 bottles had 7 bottles that weren’t full.
Using a significance level of .01, conduct a test to see if the machine
is operating properly.
10. According to Management Accounting, salary
figures for certified management accountants (CMAs) who are in the
field less than 1 year are normally distributed with a mean of $31,129. A
random sample of 15 first-year CMAs in Denver produces a mean salary of
$32,279, with a standard deviation of $1,797. Test the hypothesis that
the mean for all Denver first-year CMAs is not equal to $31,129 . Use
the .05 level of significance.
Steps for Completing Hypothesis Testing
1. H0: _____________
2. Ha: _____________
3. In words, define the random variable. __________ = ______________________
4. The distribution to use for the test is _______________________.
5. Determine the test statistic using your data.
6. Determine the p-value.
7. Do you or do you not reject the null hypothesis? Why?
8. Write a clear conclusion using a complete sentence.