Question

In: Statistics and Probability

1. In a study of vehicle ownership, it has been found that 30% of U.S. households...

1. In a study of vehicle ownership, it has been found that 30% of U.S. households do not own a vehicle, with 46% owning 1 vehicle, and the remaining owning 2 or more vehicles. The data for a random sample of 192 households in a resort community are as follows:

57 owned 0 vehicles, 104 owned 1 vehicle, and the remaining owned 2 or more vehicles.

When testing (at the 5% level of significance) whether the vehicle-ownership distribution in this community differs from that of the nation as a whole what is the test statistic? (please round your answer to 3 decimal places)

2. When testing (at the 5% level of significance) whether the vehicle-ownership distribution in this community differs from that of the nation as a whole what is the test statistic? (please round your answer to 3 decimal places)

In a study of vehicle ownership, it has been found that 29% of U.S. households do not own a vehicle, with 45% owning 1 vehicle, and the remaining owning 2 or more vehicles. The data for a random sample of 203 households in a resort community are as follows:

77 owned 0 vehicles, 106 owned 1 vehicle, and the remaining owned 2 or more vehicles.

When testing (at the 10% level of significance) whether the vehicle-ownership distribution in this community differs from that of the nation as a whole what is the critical value? (please round your answer to 3 decimal places)

Expert Solution

Que.1

We use chi-square test to the following hypothesis:

Hypothesis:

H₀ : The vehicle-ownership distribution in this community same as that of the nation.

H_a : The vehicle-ownership distribution in this community differs from that of the nation.

Observation table:

No. of vehicle	Pi	Observed freq (Oi)	Expected Freq (Ei) = Npi	(Oi - Ei)2/Ei
0	0.3	57	57.6	0.00625
1	0.46	104	88.32	2.78376812
2 or more	0.24	31	46.08	4.93503472
		192		7.72505284

Test statistic,

Where,

n = Total number of observations

s = number of parameter estimated

k= number of degrees of freedom lost due to pooling

Hence degrees of freedom = n-s-k-1 = 3 - 0-0-1 = 2

Critical value = 5.99

Since calculated value of chi-square is greater than critical value we reject null hypothesis and conclude that the vehicle-ownership distribution in this community differs from that of the nation at 5% level of significance.

Que.2

Hypothesis:

H₀ : The vehicle-ownership distribution in this community same as that of the nation.

H_a : The vehicle-ownership distribution in this community differs from that of the nation.

Observation table:

No. of vehicle	Pi	Observed freq (Oi)	Expected Freq (Ei) = Npi	(Oi - Ei)2/Ei
0	0.29	77	58.87	5.58343639
1	0.45	106	91.35	2.34945265
2	0.26	20	52.78	20.3586283
		203		28.2915173

Where,

n = Total number of observations

s = number of parameter estimated

k= number of degrees of freedom lost due to pooling

Hence degrees of freedom = n-s-k-1 = 3 - 0-0-1 = 2

Critical value = 5.99

Since calculated value of chi-square is greater than critical value we reject null hypothesis and conclude that the vehicle-ownership distribution in this community differs from that of the nation at 5% level of significance.

Critical value at 10% level of significance = 4.605

Since calculated value of chi-square is greater than critical value we reject null hypothesis and conclude that the vehicle-ownership distribution in this community differs from that of the nation at 10% level of significance.

orchestra answered 1 year ago

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