Y is regressed against X1, X2, X3, X4, X5, X6, X7, and X8. Consider the following test: Họ: B1 = B2 = B3 = B4 = Bs = 0 Hj: one or more of the restrictions under Họ does not hold The sample size n = 9000. The computer computes the heteroskedasticity-robust F-statistic for this test. The F-statistic is 2.15. What do you conclude? (R stands for reject and FTR stands for fail to reject.) R Ho at a = 0.20 R Ho at a = 0.15 R Họ at a = 0.10 R Ho at a = 0.05 R Ho at a = 0.01 R Ho at a = 0.20 R Ho at a = 0.15 R Ho at a = 0.10 R Ho at a = 0.05 FTR Ho at a = 0.01
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From the given information,
There are 5 variables restricted under null hypothesis.
That is, p=5
Numerator df=p=5
n=9000
Denominator df=n-(p+1)=9000-(5+1)=8994
P value:
F statistic=2.15
P=0.0567, obtained from the Excel function, =F.DIST.RT(2.15,5,8994).
Decision Rule:
If p-value ≤ α, then reject the null hypothesis.
If p-value > α, then do not reject the null hypothesis.
Step by step
Solved in 2 steps
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- Find Variance within the groups, and variance between the groups, and the critical valueA major oil company has developed a new gasoline additive that is supposed to increase mileage. To test this hypothesis, ten cars are randomly selected. The cars are driven both with and without the additive. The results are displayed in the following table. Can it be concluded, from the data, that the gasoline additive does significantly increase mileage? Let d=(gas mileage with additive)−(gas mileage without additive). Use a significance level of α=0.05 for the test. Assume that the gas mileages are normally distributed for the population of all cars both with and without the additive. Car 1 2 3 4 5 6 7 8 9 10 Without additive 27.2 13.7 12.5 13.4 14.7 25.5 10.3 13.9 14.5 25 With additive 29.7 15.7 14.1 16.4 17.8 27.8 12.1 15 17.3 28 Step 2 of 5: Find the value of the standard deviation of the paired differences. Round your answer to two decimal places.Random samples of resting heart rates are taken from two groups. Population 1 exercises regularly, and Population 2 does not. The data from these two samples is given below: Population 1: 66, 71, 66, 64, 63, 69, 70 Population 2: 77, 74, 69, 73, 74, 78, 68, 68 Is there evidence, at an a = 0.065 level of significance, to conclude that there those who exercise regularly have lower resting heart rates? Carry out an appropriate hypothesis test, filling in the information requested. A. The value of the standardized test statistic: -4.87322 B. The p-value is .00001 C. Your decision for the hypothesis test: A. Do Not Reject H₁. B. Do Not Reject Ho. C. Reject H₁. OD. Reject Ho.