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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

Data from the department of motor vehicles indicate that 80% of all licensed drivers are older than age 25.

  • a. In a sample of n = 60 people who recently received speeding tickets. 38 were older than 25 years and the other 22 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = .05.
  • b. In a sample of n = 60 people who recently received parking tickets. 43 were older than 25 years and the other 17 were age 25 or younger. Is the age distribution for this sample significantly different from the distribution for the population of licensed drivers? Use α = .05.

a.

To determine

To find: The age distribution for the given sample is significantly different from the distribution for the population of licensed drivers.

Explanation

Given info:

In a sample of 60 people who received speeding tickets, 38 were of age 25 and older and 22 were of age 25 and younger. Data from the Department of Motor Vehicles indicate

that 80% of all licensed drivers are older than age 25, use α=0.05.

Calculation:

Step 1:

Null Hypothesis:

H0: Age distribution for the given sample is not significantly different from the distribution for the population of licensed drivers.

Alternate Hypothesis:

H1: Age distribution for the given sample is significantly different from the distribution for the population of licensed drivers.

Step 2: For the given sample, degrees of freedom equals:

df=(C1)   where C equals number of categories=21=1

With α=0.05 and df=1, the critical value (CV)  is obtained from the χ2table as

χ2=3.841

Step 3: χ2statistics is calculated as:

χ2=(fofe)2fe

The proportion of licensed driver older than 25 is 0.8(that is, 80%) and proportion of those younger than 25 is 0.2.

The formula to calculate expected frequency is:

fe=p×n

Substituting respective values of proportion and n=60 in the above formula:

fe,25+=0

b.

To determine

To find: The age distribution for the given sample is significantly different from the distribution for the population of licensed drivers.

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