I am wondering if there's a mistake in this video in the slide at 3m3s. Should the "less" in "the probability of getting a mean of 68.7 or less from a sample of this size is 0.18" actually be "more"?

In this example 0.18 is the p-value, and H0 is that the mean weight of peanuts in chocolate bars is 70 grams. Assume "0.18" was actually "1", then the probability of getting a mean of 68.7 or less would be 100%. Then wouldn't the null hypothesis clearly be rejected: chocolate bars do in fact on average have less than 70 grams of nuts?

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    $\begingroup$ No, I don't think so. The definition of a p-value is the probability, under the null hypothesis, of observing the same or a more extreme result. In this case, the more extreme result is below 68.7, which is in turn below 70. Hence it would be less. This corresponds to the 1-sided test below the mean. $\endgroup$ – NatWH May 24 '18 at 13:40
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    $\begingroup$ Plus I think you're thinking about p-values incorrectly. If the p-value was 1, it would indicate that a value of 68.7 from a sample is a certainty if the null hypothesis (the population mean = 70) were true. The p-value always refers to a probability under the null hypothesis. Hence it is small p-values, i.e. very unlikely results if the null hypothesis is true, which cause a rejection of the null hypothesis. $\endgroup$ – NatWH May 24 '18 at 13:43
  • $\begingroup$ If the null is equal to 68.7 the test is two-sided. $\endgroup$ – Michael R. Chernick May 24 '18 at 14:21
  • $\begingroup$ This may help. stats.stackexchange.com/questions/406593/understanding-p-value $\endgroup$ – user2889674 Jun 24 '19 at 17:20

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