Hypothesis Testing

CH. 8 WHITEBOARD REVIEW

A random sample of 1088 adults between the ages of 18 and 44 is conducted. It found that 261 of the 1088 adults smoke. Use a 0.05 significance level to test the claim that less than ¼ of such adults smoke.

Null /Alternative Hypothesis:Significance Level:Test Statistic:

P-Value:

Conclusion:

PROBLEM 1:

When planning for construction of a parkway, engineers must consider the weights of cars to be sure that the road surface is strong enough. A simple random sample of 32 cars yields a mean of 3605.3lb and a standard deviation of 501.7lb. Use a 0.01 significance level to test the claim that the weight of cars is less than 3700lb.

Null /Alternative Hypothesis:Significance Level:Test Statistic:

P-Value:

Conclusion:

PROBLEM 2:

A simple random sample of 32 cars yields a mean weight of 3605.3lbs, a standard deviation of 501.7lb, and the sample weights appear to be from a normally distributed population. Use a 0.01 significance level to test the claim that the standard deviation of the weights of the cars is less than 520lb.

Null /Alternative Hypothesis:Significance Level:Test Statistic:

P-Value:

Conclusion:

PROBLEM 3:

List below are winning times (in seconds) of women in the 100-meter dash for consecutive summer Olympic games. Assume that the times are sample data from a larger population. Test the claim that the mean winning time is less than 11 seconds. Use a 0.05 signifi cance level. What can we conclude about winning times in the future?

11.07 11.08 11.06 10.97 10.54 10.82 10.94 10.75 10.93

Null /Alternative Hypothesis: Signifi cance Level: Test Statistic:

P-Value:

Conclusion:

PROBLEM 4:

An axial load of an aluminum can is the maximum weight that the sides can support before collapsing. The axial load is an important measure because the top lids are pressed onto the sides with pressure that vary between 158lb and 165lb. Pepsi experimented with a thinner can, and a random sample of 175 of the thinner cans had a mean of 267.1lb and a standard deviation of 22.1lb. Use a 0.01 signifi cance level to test the claim that the thinner cans have a mean axial load that is less than 281.8lb, which is the mean axial load of the thicker cans that were in use.

Null /Alternative Hypothesis: Signifi cance Level: Test Statistic:

P-Value:

Conclusion:

PROBLEM 5:

A supplier of digital memory cards claims that less than 1% of the cards are defective. In a random sample of 400 memory cards, it is found that 3% are defective, but the supplier claims that this is only a sample fluctuation. At the .01 significance level, test the supplier’s claim.

Null /Alternative Hypothesis:Significance Level:Test Statistic:

P-Value:

Conclusion:

PROBLEM 6:

When designing a movie theater with stadium seating, engineers decide to consider the sitting eye heights of women. In a random sample of 50 women, their heights had a mean of 739mm. Assuming is known to be 33mm and using a .05 signifi cance level, what is the probability that their mean sitting heights is less than 730mm?

Null /Alternative Hypothesis: Signifi cance Level: Test Statistic:

P-Value:

Conclusion:

PROBLEM 7:

****None of the whiteboard problems had an alternative hypothesis with a greater than (>) symbol. What is done diff erently with those types of problems?

STUDY!Make cheat sheet.Bring calculator.

TEST TOMORROW!!!

HOMEWORK