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Fewer than 5% of adults ride the bus to work in Los Angeles.

I thought for this null hypothesis is, Ho: p < 0.05, Ha: p >= 0.05, but the answer says I am wrong. Kindly help with this.

similarly for this question The chance of developing breast cancer is under 11% for women. Ho: p < 0.11 and Ha: p >= 0.11, is that correct. Please provide assistance

Reference, I found these in this website, https://stats.libretexts.org/Bookshelves/Introductory_Statistics/Book%3A_Introductory_Statistics_(OpenStax)/09%3A_Hypothesis_Testing_with_One_Sample/9.E%3A_Hypothesis_Testing_with_One_Sample_(Exercises)

question no e and i

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    $\begingroup$ The alternative is what you’re trying to prove. Perhaps you can try again with this in mind. // $5\%$ is $0.05$, not $0.5$. // Please add the self-study tag. $\endgroup$
    – Dave
    Feb 7 at 15:53
  • $\begingroup$ By mistake I've typed 0.5, it is 0.05. In this page, for the questions e and i, stats.libretexts.org/Bookshelves/Introductory_Statistics/… $\endgroup$
    – xojiv
    Feb 7 at 16:03
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    $\begingroup$ Null hypothesis in such problems must always contain $=,$ perhaps as $\le, \ge$ or just $=.$ Parameter value for $=$ determines the null distribution. $\endgroup$
    – BruceET
    Feb 7 at 17:30
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H0: p >= 0.05 Ha: p < 0.05

Statistical tests don´t try to back the thing you are interested in, but rather try to dismiss it. This approach holds true to the idea of falsification. This means researchers should try to disprove their hypothesis rather than try to prove it. By defining the hypothesis you are interested in as the alternative hypothesis you make sure that it is hard to be convinced that Ha has better evidence than H0.

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