Question

A highway patrol officer believes that the average speed of cars traveling over a certain segment of freeway actually exceeds 70 mph (where the posted speed limit is 65 mph). A random sample of 16 cars had their speeds measured by radar. The results are shown below. Use α=0.05, can we conclude that the officer's belief is correct? Repeat the question and test if the average speed exceeds the speed limit. 81, 72, 69, 78, 65, 75, 65, 70, 64, 77, 70, 75, 73, 76, 67, 66 

          A highway patrol officer believes that the average speed of cars traveling over a certain segment of freeway actually exceeds 70 mph (where the posted speed limit is 65 mph). A random sample of 16 cars had their speeds measured by radar. The results are shown below. Use α=0.05, can we conclude that the officer's belief is correct? Repeat the question and test if the average speed exceeds the speed limit. 81, 72, 69, 78, 65, 75, 65, 70, 64, 77, 70, 75, 73, 76, 67, 66
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Elementary Statistics a Step by Step Approach
Elementary Statistics a Step by Step Approach
Allan G. Bluman 9th Edition
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A highway patrol officer believes that the average speed of cars traveling over a certain segment of freeway actually exceeds 70 mph (where the posted speed limit is 65 mph). A random sample of 16 cars had their speeds measured by radar. The results are shown below. Use α=0.05, can we conclude that the officer's belief is correct? Repeat the question and test if the average speed exceeds the speed limit. 81, 72, 69, 78, 65, 75, 65, 70, 64, 77, 70, 75, 73, 76, 67, 66
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A highway patrol officer believes that the average speed of cars traveling over a certain stretch of highway exceeds the posted limit of 55 km/ hr. A random sample of 10 cars had their speeds measured by radar. The results in Km / hr are as follows: 71, 53, 62, 49, 59, 52, 58, 61, 85, 55 Do these data provide sufficient evidence to support the highway patrol belief, at the 10% level of significance? Measurements are made on a random sample of 100 components drawn from a population of size 1546 and having a standard deviation of 2.93 mm. The mean measurement of the components in the sample is 67.45 mm. Determine: The standard error of the mean The 99% confidence limits for an estimate of the mean of the population

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Transcript

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00:01 We are given that a certain speed that's on a highway are 55 kilometers per hour, and the officer think it's greater than that.
00:08 So we are going to set up our null and alternative hypothesis.
00:13 Our null is that the speeds are actually 55 kilometers per hour, and our alternative is going to be that we think the speeds of the cars are greater than 55 miles per hour.
00:24 We are setting our significance level at 10 percent, and we know we have not.
00:30 9 degrees of freedom because we have 10 pieces of data.
00:33 What we're going to do is we're going to run a one prop or just a t test to find out the probability that the speeds are greater than 55.
00:45 To do that, we're going to need to find the mean of our sample.
00:49 If we add all these numbers up and divide by 10, we get that it's equal to 60 .5.
00:58 Our standard deviation of this sample is 10.
01:03 What we want to do is we now want to go through and find the t score for this value...
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