A psychologist believes that 77% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 34 male drivers and asked each what they did when lost. If the belief is true, determine the probability that less than 70% said they continue driving.

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A psychologist believes that 77% of male drivers when lost continue to drive, hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 34 male drivers and asked each what they did when lost. If the belief is true, determine the probability that less than 70% said they continue driving.

 

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Concepts and reason

The concept of probability and one sample proportion is used to solve this problem. Probability measures he chance of occurrence of an event and it is a positive number which takes value between 0 and 1 A one sample proportion defines the proportion of the sample values possessing a particular characteristic The proportion is the ratio of the number of individuals in the sample possessing the characteristic to the total number of individuals in the sample.

Fundamentals

For a sample of size n. if x number of sample observation possess a specific characteristic then the sample proportion p is calculated as

.p=xn

The z-statistic for a hypothesized proportion p0

z=p-p0p0q0n

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