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Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570

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BuyFindarrow_forward

Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
ISBN: 9781133956570
Textbook Problem

The average age for licensed drivers in the county is μ = 40.3 years with a standard deviation of σ = 13.2 years.

  1. a. A researcher obtained a random sample of n = 16 parking tickets and computed an average age of M = 38.9 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = 16 people is a representative sample of licensed drivers?
  2. b. The same researcher obtained a random sample of n = 36 speeding tickets and computed an average age of M = 36.2 years for the drivers. Compute the z-score for the sample mean and find the probability of obtaining an average age this young or younger for a random sample of licensed drivers. Is it reasonable to conclude that this set of n = 36 people is a representative sample of licensed drivers?

(a)

To determine

To find: The z-score for the sample mean.

To find: The probability of obtaining an average age this young or younger for a random sample of licensed drivers

To check: Whether it is reasonable to conclude the set of n=16 people is a representative sample of licensed drivers.

Explanation

Given info:

The average age for licensed drivers in the country is μ=40.3 and σ=13.2.

The sample mean is and the random sample is, n=16.

Calculation:

The z-score is used to transform any distribution in to standardized distribution with a predetermined mean and a predetermined standard deviation.

The formula to find the z-Score is,

z=MμσM

Where, σM=σn

Substitute the value 40.3 for μ, 13.2 for σ, 16 for n and 38.9 for M as,

z=38.940.313.216=0

(b)

To determine

To find: The z-score for the sample mean.

To find: The probability of obtaining an average age this young or younger for a random sample of licensed drivers.

To check: Whether it is reasonable to conclude the set of n=36 people is a representative sample of licensed drivers.

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