Question

It has been reported that 8.7% of U.S. households do not own a vehicle, with 33.1% owning 1 vehicle, 38.1% owning 2 vehicles, and 20.1% owning 3 or more vehicles. The data for a random sample of 100 households in a resort community are summarized in the frequency distribution below. At the 0.05 level of significance, can we reject the possibility that the vehicle-ownership distribution in this community differs from that of the nation as a whole?
Number of Vehicles Owned Number of Households 0 20 1 35 2 23 3 or more 22 =100

Answer 1

Answer:

Here, the test statistics ( 20.951 ) is greater than the critical value ( 7.815 )

Therefore, we reject H₀ at 0.05 level of significance.

Hence, there is significant evidence to support the claim that In this community, vehicle ownership distribution is NOT like that of all U.S household

Step-by-step explanation:

Given the data in the question;

Number of vehicle owned                 Number of households

0                                                             20

1                                                              35

2                                                             23

3 or more                                               22

Total ( n )                                               100

so

Null hypothesis           H₀ : In this community, vehicle ownership distribution is like that of all U.S household

Alternative hypothesis Hₐ : In this community, vehicle ownership distribution is NOT like that of all U.S household

Also given that, ∝ = 0.05

Now, we compute the test statistics;

x² = ∑[ ( O$_i$ - E$_i$ ) / E$_i$ ]

where E$_i$ is expected frequency and O$_i$ is observed frequency.

so we make our table for chi square test statistics

No. of                 O$_i$            P                E$_i$            (O$_i$ - E$_i$)²             (O$_i$ - E$_i$)²/E$_i$

Vehicle                                              (n×P)

owned

0                        20         0.087          8.7            127.69                 14.677

1                         35         0.331           33.1            3.61                     0.109

2                        23         0.381           38.1           228.01                 5.985

3 or more          22         0.201          20.1           3.61                      0.180

Total                  100                           100                                        20.951

hence, x² = 20.951

Now, degree of freedom df = k - 1 = 4 - 1 = 3

From Chi-Square critical value table; ( right tailed test ) for ∝ = 0.05

$x_{0.05, 3$ = 7.815

Decision Rule

Reject H₀ if x² is greater than xₐ².

Here, the test statistics ( 20.951 ) is greater than the critical value ( 7.815 )

Therefore, we reject H₀ at 0.05 level of significance.

Hence, there is significant evidence to support the claim that In this community, vehicle ownership distribution is NOT like that of all U.S household