Statistics and the TI-84
Practice Problems 10 : One population Hypothesis Testing
1. The average height of females in a certain college class has been 162 centimeters with a standard
deviation of 7 centimeters. Is there reason to believe that there has been a change in the average height if
a random sample of 49 females in the present freshman class has an average height of 166 centimeters.
Use a 0.01 level of significance.
Show all the required steps and give a precise conclusion.
Step 1. State Ho: ________________
Step 2. Type of test; _________
State H1: ___________________________
Step 3. Level of significance: __________
Step 4. critcal value of the statistic: _____
Step 5. Diagram
Step 6. Decision rule: ______________________________
Step 7. Compute the statistic.: __________________
Compute the p-value
Step 8. Conclusion:
p-value: ___________
______________________________________________________
2. A random sample of 9 cigarettes of a certain brand has an average nicotine content of 4.2 milligrams
and a standard deviation of 1.5 milligrams. Is this in line with the manufacturer's claim that the average
nicotine content does not exceed 3.4 milligrams? Use a 0.01 level of significance and assume the
distribution of nicotine contents to be normal. Show all the required steps and give a precise conclusion.
Step 1. State Ho: ________________
State H1: ________________________
Step 2. Type of test; __________
Step 3. Level of significance: __________
Step 4. critcal value of the statistic: _____
Step 5. Diagram
Step 6. Decision rule: ________________________________
Step 7. Compute the statistic.: __________________
Compute the p-value
Step 8. Conclusion:
p-value: ___________
______________________________________________________
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3. It is believed that less than 60% of the residents in a certain area favor an annexation suit by a
neighboring city. What conclusion would you draw if only 110 in a sample of 200 voters favor the suit?
Use a 0.04 level of significance.
Step 1. State Ho: ____________________
State H1: __________________
Step 2. Type of test; __________
Step 3. Level of significance: _________
Step 4. critcal value of the statistic: _____
Step 5. Diagram
Step 6. Decision rule: ________________________________
Step 7. Compute the statistic.: __________________
Compute the p-value
p-value: ___________
Step 8. Conclusion: ______________________________________________________
4. A food company is planning to market a new type of product. However, before marketing this product ,
the company wants to find what percentage of the people like it.
The company’s management has decided that it will market the new product only if at least 35% of the
people like it. The company’s research department selected a random sample of 400 persons and asked
them to try the new product . Of these 400 persons, 112 said they liked it. Testing at the 2.5 %
significance level , can you conclude that the company should market this new productt?
Step 1. State Ho: ____________________ State H1: _______________________
Step 2. Type of test __________
Step 3. Level of significance: _______
Step 4. critcal value of the statistic: ________________________
Step 5. Diagram
Step 6. Decision rule:
Step 7. Compute the statistic.: __________________
Compute the p-value
p-value: ___________
______________________________________________________
______________________________________________________
Step 8. Conclusion:
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5. According to a Census survey taken , American workers aged 30 to 45 spent an average of 22
minutes traveling to work . A recently taken random sample of 20 American workers in this age group
yielded a mean commuting time to work equal to 25 minutes with a standard deviation of 8 minutes.
Assume that the times to commute to work for all such workers are normally distributed. Using a 5 %
significance level, can you conclude that the current mean travel times to work for all U.S. workers ages
30 to 445is different than 22 minutes?
Step 1. State Ho: _________________________
State H1: ______________________________
Step 2. Type of test; __________
Step 3. Level of significance: __________Step 4. critcal value of the statistic: _____
Step 5. Diagram
Step 6. Decision rule: ________________________________
Step 7. Compute the statistic.: __________________
Compute the p-value
p-value: ___________
Step 8. Conclusion: ______________________________________________________
______________________________________________________
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