title: For what sample mean would the p-value be equal to 0.05
body: <p>It's a homework question. I am not looking for exact answer but need a direction. I have following question</p>
  
  <p>H0: µ = 30<br>
  HA: µ != 30  </p>
  
  <p>We know that the sample standard deviation is 10 and the sample size is 70. For what sample mean would the p-value be equal to 0.05? Assume that all conditions necessary for inference are satisfied.</p>
  
  <p>I am solving it as following</p>
  
  <p>As our H0 is based on equal sign, so our test is two sided, we need to check both for small and larger values.<br>
  The P value of 0.05 in the probability table is equal to a z score of 1.65.
  We need to calculate S.E and then find mean using Z formula </p>
  
  <pre><code>S.D = 10
  n = 70
  se &lt;- S.D/sqrt(n)
  # Z= (xbar- µ)/ S.E =&gt; xbar = Z * S.E + µ
  xbar = (1.65*se)+30
  </code></pre>
  
  <p>So, in this way i get one mean value. but our test is two sided. so i need another mean value. I am not getting how can I solve it. Any suggestion or idea will be appreciable.
  Thanks</p>