The horsepower (Y, in bhp) of a motor car engine was measured at a chosen set of values of running speed (X, in rpm). The data are given below (the first row is the running speed in rpm and the second row is the horsepower in bhp): rpm 1100 1400 1700 2300 2700 3200 3500 4000 4600 5200 5600 6100 Horsepower (bhp) 50.2 64.29 67.83 98.56 131.09 163.65 161.55 198.62 226.03 254.71 283.63 299.81 The mean and sum of squares of the rpm are 3450.0000 rpm and 173900000.0000 rpm 22 respectively; the mean of the horsepower values is 166.6642 bhp and the sum of the products of the two variables is 8506152.0000 rpm bhp. Given Values: a) Slope: 0.052 b) Intercept: -11.694 c) 95% Confidence Interval when the standard error of the estimate of the slope coefficient was found to be 0.001160: (0.0494, 0.0546) please answer the following: Part e) Without extending beyond the existing range of speed values or changing the number of observations, we would expect that increasing the variance of the rpm speeds at which the horsepower levels were found would make the confidence interval in (c) A. narrower. B. either wider or narrower depending on the values chosen. C. unchanged. D. wider. Part f) If testing the null hypothesis that horsepower does not depend linearly on rpm, what would be your test statistic? (For this part, you are to calculate the test statistic by hand using appropriate values from the answers you provided in part (a) accurate to 3 decimal places, and values given to you in part (c).) Answer: Part g) Assuming the test is at the 1% significance level, what would you conclude from the above hypothesis test? A. Since the observed test statistic falls in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we can reject the null hypothesis that the horsepower does not depend linearly on rpm. B. Since the observed test statistic does not fall in either the upper or lower 1 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm. C. Since the observed test statistic does not fall in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm. D. Since the observed test statistic does not fall in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we can reject the null hypothesis that the horsepower does not depend linearly on rpm. E. Since the observed test statistic falls in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm.
The horsepower (Y, in bhp) of a motor car engine was measured at a chosen set of values of running speed (X, in rpm). The data are given below (the first row is the running speed in rpm and the second row is the horsepower in bhp):
| rpm | 1100 | 1400 | 1700 | 2300 | 2700 | 3200 | 3500 | 4000 | 4600 | 5200 | 5600 | 6100 |
| Horsepower (bhp) | 50.2 | 64.29 | 67.83 | 98.56 | 131.09 | 163.65 | 161.55 | 198.62 | 226.03 | 254.71 | 283.63 | 299.81 |
The mean and sum of squares of the rpm are 3450.0000 rpm and 173900000.0000 rpm 22 respectively; the mean of the horsepower values is 166.6642 bhp and the sum of the products of the two variables is 8506152.0000 rpm bhp.
Given Values:
a) Slope: 0.052
b) Intercept: -11.694
c) 95% Confidence Interval when the standard error of the estimate of the slope coefficient was found to be 0.001160: (0.0494, 0.0546)
please answer the following:
Part e)
Without extending beyond the existing
A. narrower.
B. either wider or narrower depending on the values chosen.
C. unchanged.
D. wider.
Part f)
If testing the null hypothesis that horsepower does not depend linearly on rpm, what would be your test statistic? (For this part, you are to calculate the test statistic by hand using appropriate values from the answers you provided in part (a) accurate to 3 decimal places, and values given to you in part (c).)
Answer:
Part g)
Assuming the test is at the 1% significance level, what would you conclude from the above hypothesis test?
A. Since the observed test statistic falls in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we can reject the null hypothesis that the horsepower does not depend linearly on rpm.
B. Since the observed test statistic does not fall in either the upper or lower 1 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm.
C. Since the observed test statistic does not fall in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm.
D. Since the observed test statistic does not fall in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we can reject the null hypothesis that the horsepower does not depend linearly on rpm.
E. Since the observed test statistic falls in either the upper or lower 1/2 percentiles of the t distribution with 1010 degrees of freedom, we cannot reject the null hypothesis that the horsepower does not depend linearly on rpm.
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