Why do we say we fail to reject the null hypothesis instead


Your local public library reported last year that the average number of children visiting the library each day was 77. You would like to test whether that has changed.

1. Now consider Scenario C. You randomly choose 25 days and count the number of children visiting the library on those days. The average for your sample is 63. You also know that the population standard deviation for children visiting the library is 29. Test whether the number of children visiting the library has changed from the previous year using .

2. Why do we say "we fail to reject the null hypothesis" instead of "we accept the null hypothesis"?

3. What do we call the probability of a Type I error?

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