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Chapter 4: Q38 (page 146)

Using Probability to Form Conclusions. In Exercises 37鈥�40, use the given probability value to determine whether the sample results could easily occur by chance, then form a conclusion.

Buckle Up A study of the effect of seatbelt use in head-on passenger car collisions found that drivers using a seatbelt had a 64.1% survival rate, while drivers not using a seatbelt had a 41.5% survival rate. If seatbelts have no effect on survival rate, there is less than a 0.0001 chance of getting these results (based on data from 鈥淢ortality Reduction with Air Bag and Seat Belt Use in Head-on Passenger Car Collisions,鈥� by Crandall, Olson, Sklar, American Journal of Epidemiology, Vol. 153, No. 3). What do you conclude?

Short Answer

Expert verified

The probability of getting the given sample results by chance equal to 0.0001 is significantly low. Thus, it can be said that the sample results do not occur by chance.

Since sample results do not occur by chance, it can be concluded that wearing a seat belt helps prevent deaths among car drivers.

Step by step solution

01

Given information

There is a 64.1% survival among drivers who use seat belts.

There is a 41.5% survival among drivers who do not use seat belts.

The probability that these results occur by chance is less than 0.0001.

02

Interpreting probability value 

The measure of the likelihood of a result is provided by itsprobability value.

Its value ranges from 0 to 1.

If a value is considerably low (lower than 0.05), the event has a low chance of occurring.

03

Concluding the result

Assuming the condition that seatbelts do not affect the survival rate, it is stated that the sample results have a 0.0001 probability of occurring.

This implies that 1 in 10,000 results occur by chance.

Theprobabilityvalue isvery low, and hence the chance of the results are not obtained by chance.

As the probability that the results have occurred by chance is extremely low, it can be concluded that there is sufficient evidence to accept the condition that the use of seatbelts can affect the survival rate of drivers.

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Most popular questions from this chapter

Probability from a Sample Space. In Exercises 33鈥�36, use the given sample space or construct the required sample space to find the indicated probability.

Three Children Use this sample space listing the eight simple events that are possible when a couple has three children (as in Example 2 on page 135): {bbb, bbg, bgb, bgg, gbb, gbg, ggb, ggg}. Assume that boys and girls are equally likely, so that the eight simple events are equally likely. Find the probability that when a couple has three children, there is exactly one girl.

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惭肠顿辞苍补濒诲鈥檚

Burger King

奥别苍诲测鈥檚

Taco Bell

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329

264

249

145

OrderNotAccurate

33

54

31

13

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a. 60% of the author鈥檚 region will get rain today.

b. In the author鈥檚 region, it will rain for 60% of the day.

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Probability from a Sample Space. In Exercises 33鈥�36, use the given sample space or construct the required sample space to find the indicated probability.

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