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A random sample of three-year-old thoroughbred racehorses is taken, and the 95% confidence interval for the true mean height (in inches) is calculated to be (62.0, 68.4). Data about horses from the historical record of the three-year old thoroughbred racehorses who have run in the Kentucky Derby is examined, and the mean height is calculated to be 68.25 inches. Does this sample provide convincing evidence that three-year-old thoroughbred racehorses are, on average, shorter than those that run in the Kentucky Derby

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Options :

Yes, 68.25 is near the top of the confidence interval.

Yes, the value of 68.25 is a number in the confidence interval.

Yes, 68.25 is much higher than the sample mean of all three-year-old thoroughbred racehorses, which was 65.2 inches.

No, the value of 68.25 is a number in the confidence interval.

No, the horses that run in the Kentucky Derby are a subset of all three-year-old thoroughbred racehorses

Answer:

No , the value of 68.25 is a number in the confidence interval.

Step-by-step explanation:

The confidence interval gives a range if values which is used in establishing the significance of an hypothesis. If the true mean falls within the confidence interval drawn, then our finding is insignificant and the null hypothesis will stand. However, if the true mean does not fall within the interval, then our result is considered significant and the null is thus rejected.

Since true mean exists within the confidence interval, then we conclude that the sample does not provide convincing evidence that three-year-old thoroughbred racehorses are, on average, shorter than those that run in the Kentucky Derby

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