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1.  

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz.



2.  

Assume that the data has a normal distribution and the number of observations is greater than fifty. Find the critical z value used to test a null hypothesis.



3.  

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim.

The owner of a football team claims that the average attendance at games is over 642, and he is therefore justified in moving the team to a city with a larger stadium. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is failure to reject the null hypothesis, state the conclusion in nontechnical terms.

There is not sufficient evidence to support the claim that the mean attendance is greater than 642.
There is sufficient evidence to support the claim that the mean attendance is less than 642.
There is sufficient evidence to support the claim that the mean attendance is greater than 642.
There is not sufficient evidence to support the claim that the mean attendance is less than 642.


4.  

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test.

An entomologist writes an article in a scientific journal which claims that fewer than 11 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Identify the type I error for the test.

The error of rejecting the claim that the true proportion is at least 11 in ten thousand when it really is at least 11 in ten thousand.
The error of failing to reject the claim that the true proportion is at least 11 in ten thousand when it is actually less than 11 in ten thousand.
The error of rejecting the claim that the true proportion is less than 11 in ten thousand when it really is less than 11 in ten thousand.


5.  

A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 5 in every one thousand. Identify the type II error for the test.

The error of rejecting the claim that the true proportion is less than 5 in one thousand when it really is less than 5 in one thousand.
The error of failing to reject the claim that the true proportion is at least 5 in one thousand when it is actually less than 5 in one thousand.
The error of rejecting the claim that the true proportion is at least 5 in one thousand when it really is at least 5 in one thousand.


6.  

Use the given claim and test statistic to find the P-value.

Claim: The mean monthly salary of employees at one company is at most $32,500.

Test statistic: z = 0.52

0.6985
0.6030
0.3015
0.3970


7.  

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.

Reject H0 if test statistic < 2.05.
Reject H0 if test statistic > -2.05.
Reject H0 if test statistic < -2.05.
Reject H0 if test statistic < -2.33.


8.  

Compute the value of an appropriate test statistic for the given hypothesis test.

z = 4.59
z = 33.09
z = 0.64
z = -4.59


9.  

0.8869
0.9370
0.0630
0.1131


10.  

Find the critical t value or values for the given hypothesis, sample size, and significance level.

-2.650
-2.681
2.681
2.650


11.  

Should the statistician use a t distribution, a normal distribution, or neither to test the null hypothesis?

t distribution
Normal distribution
Neither


12.  

What decision rule should you use to test H0?



13.  

Compute the value of an appropriate test statistic for the given hypothesis test.

A cereal company claims that the mean weight of the cereal in its packets is at least 14 oz. You wish to test this claim at the 0.02 level of significance. The mean weight for a random sample n = 12 cereal packets is 13.4 ounces with a standard deviation of 0.8 ounces. Compute the value of the appropriate test statisic.

t = -2.60
t = -9.00
t = 2.60
t = -0.75


14.  

Solve the problem.



15.  

State the decision rule to test the null hypothesis.

A radio show producer believes that a new proposed format would be preferred by only 15% of their current listeners. A survey of 100 current listeners showed that 18% favored the new format. Does the producer know his business? H0: p = 0.15. Confidence level: 99%.



16.  

Compute the test statistic used to test the null hypothesis.

1.425
1.038
1.549
2.076


17.  

Find the P-value for the indicated hypothesis test.

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. Find the P-value for a test of the researcher's claim.

0.0038
0.0019
0.0015
0.0529


18.  

Find the critical value or values of X2 based on the given information.

31.526
8.907
7.015
8.231


19.  

Determine the decision criterion for rejecting the null hypothesis in the given hypothesis test; i.e., describe the values of the test statistic that would result in rejection of the null hypothesis.

A manufacturer produces steel rods which average 40 cm in length and claims that the lengths of the steel rods have a standard deviation smaller than 0.26 cm. A random sample of 18 steel rods resulted in lengths with a standard deviation of 0.21 cm. In a hypothesis test of the manufacturer's claim, what criterion would be used for rejecting the null hypothesis if the significance level is alpha = 0.025?

Reject H0 if test statistic < 8.231.
Reject H0 if test statistic < 7.564.
Reject H0 if test statistic > 31.526.
Reject H0 if test statistic > 30.191.

   


© 2000 by Addison Wesley Longman
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