The table lists the distance d (in ft) above the ground for an object dropped in a vacuum from a height of 500 feet. The time t
(in sec) is the time after the object has been released. Use technology to find the correct R2 value of the given data using a quadratic regression.
2 answers:
Answer:
The correct option is 4. The value of R² is 1.000.
Step-by-step explanation:
The table lists the distance d (in ft) above the ground for an object dropped in a vacuum from a height of 500 feet. The time t (in sec) is the time after the object has been released.
The general form of quadratic regression is
Use technology, we get
The required quadratic regression is
The value of R² is 1.000. Therefore the correct option is 4.
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Answer:
And rounded up we have that n=350
Step-by-step explanation:
Previous concepts
A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the real population proportion of interest
represent the estimated proportion for the sample
n is the sample size required (variable of interest)
represent the critical value for the margin of error
Solution to the problem
The population proportion have the following distribution
In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 95% of confidence, our significance level would be given by and
. And the critical value would be given by:
The margin of error for the proportion interval is given by this formula:
(a)
And on this case we have that and we are interested in order to find the value of n, if we solve n from equation (a) we got:
(b)
And replacing into equation (b) the values from part a we got:
And rounded up we have that n=350