LGU+ 12:30 AM . A rental car company wants to investigate whether the type of ca

Question

LGU+ 12:30 AM . A rental car company wants to investigate whether the type of car rented affects the lengtih of the rental period. An experiment is run for one week at a particular location, and 5 rental contracts are selected at random for each car type. T manufacturers are shown in the followin. Table 3. Note that h = 4.6, 3.4. -62, = 2.75, 2 = 4 he results according to car ,= 4.25, 55, fs-6.25, and 4.55. Statistical Manufacture Type of Car 1 2 3 4 5 Sub-compact 2 5 3 7 6 Compact 1 34 5 4 Midsize 42 3 5 6 Full Size 46 7 5 9 Table 3: Observations for Problem 4 software produced the following ANOVA table (Table 4) SS dof MS F p-value Source Type of Car 21.75 3 7.25 40460.033 Manufacture 29.74 7.425 4.144 Err Tot 21.5 12 1.79 72.95 19 Table 4: ANOVA Table for 4 (a) is there evidence to support a claim that the type of car rented affects the length of (b) Is there evidence to claim that the manufacturer type affects the length of the rental (c) Is the effect of the "Full Size" car type different from that of the "Sub-compact" car the rental contract? Use = 0.05, (5 points] contract? Use =0.05. [5 points! type by the Tukey test? Use a-0.05. Refer to gaosan points 4.20, gtasas = 4.05. I5 (d) It turns out that Manufactures 1 and 2 are from domestic companies and Manufactures 4and 5 are from foreign companies. Compare the effects of domestic Manufactures and

Explanation / Answer

1.

The tests are done with respect to the null that the type of the car rented have no affects on the length of the rental contract against the alternative that they have affect on each other.

Now the table gives the information of everything.

Here the test statistics followa a non-central F distribution when the null hypothesis is true and it is given by F=MST/MSE; Where MST: Mean square of treatments= 7.25 and MSE: Mean square of error= 1.79

Hence the p-value is given by 2*min(P(F>f), P(F<f)). where f=value of the test statistics from the data.

the value of the test statistic is 4.046 hence the p value is 0.033 which is less than 0.05 and our conjecture inclines towards the alternative.

i.e. we can conclude that the type of the car rented have some affects on the length of the rental contract.

2.

The tests are done with respect to the null that the manufacturer type have no affects on the length of the rental contract against the alternative that they have affect on each other.

Now the table gives the information of everything.

Here the test statistics followa a non-central F distribution when the null hypothesis is true and it is given by F=MST/MSE; Where MST: Mean square of treatments= 7.425 and MSE: Mean square of errors= 1.79

Hence the p-value is given by 2*min(P(F>f), P(F<f)). where f=value of the test statistics from the data.

the value of the test statistic is 4.144 hence the p value is 0.0245(obtained by putting the value of f in the abhove formulae of p-value) which is less than 0.05 and our conjecture inclines towards the alternative.

i.e. we can conclude that the manufacturer type have some affects on the length of the rental contract.

3.

Here we are willing to test that the effect of full size car type and the subcompact car type are same vs the alternative that they are different.

the test stat is given by t=(y1.-y4.)/(MSE*sqrt(2/5)); which follows a t stat with df of the error i.e. 12 and is a both sided test.

i.e. we accept the alternative if |observed(t)|>t.025,12 . t.025,12 is the upper 2.5 percentile point of a non-central t distribution with df 12.

t.025,12 =2.178 and |observed(t)|=1.413

Hence we conclude that the effect of full size car type and the subcompact car type are same.

4.

incomplete question. provide full question to get correct answer.

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