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I have a question about a disagreement between a hypothesis test through a p-value and a test through a confidence interval. I thought they weren't supposed to disagree.

The problem is the following (I think its from a textbook from Rice Uni):

  • "Registered nurses earned an average annual salary of 69,110. For that same year, a survey was conducted of 41 California registered nurses to determine if the annual salary is higher than $69,110 for California nurses. The sample average was 71,121 with a sample standard deviation of 7,489."

Issue: based on a 0.05 significance , we reject the null that the nurses average anual salary is 69110 because the p-value is 0.0466 but based on a 95% confidence Interval we don't reject it because the interval is given approx. by: (68,757; 73,485) . What's going on here?

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    $\begingroup$ Pay attention to the difference between one-tailed and two-tailed intervals. $\endgroup$
    – whuber ♦
    Commented May 21, 2020 at 15:00
  • $\begingroup$ Of course, thus , for a 0.05% hypothesis test I need to use a 90% C.I. and so on, I'm I right? $\endgroup$
    – ceins
    Commented May 21, 2020 at 15:19
  • $\begingroup$ Yes, provided that by "0.05%" you really meant 5% :-) and by "hypothesis test" you meant a one-sided test, as in the question. $\endgroup$
    – whuber ♦
    Commented May 21, 2020 at 15:36
  • $\begingroup$ Yes whuber! that was what I meant! thank you so much for sharing your knowledge :) $\endgroup$
    – ceins
    Commented May 21, 2020 at 15:36

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