Question

Consider versus A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with Calculate the p-value. Round your answer to four decimal places.

Answer 1

Complete Question

Consider H0: μ=38 versus H1: μ>38. A random sample of 35 observations taken from this population produced a sample mean of 40.27. The population is normally distributed with σ=7.2.

Calculate the p-value. Round your answer to four decimal places.

Answer:

The   $p-value = 0.030742$

Step-by-step explanation:

From the question we are told that

  The population mean is  $\mu = 38$

   The sample size is  n = 35

   The sample mean is  $\= x = 40.27$

   The standard deviation is  $\sigma = 7.2$

The null  hypothesis is  $H_o$: μ=38

The alternative hypothesis is H1: μ>38

Generally the test statistics is mathematically represented as

      $t = \frac{ \= x -\mu }{\frac{\sigma }{ \sqrt{n} } }$

=>    $t = \frac{ 40.27 - 38 }{\frac{ 7.2 }{ \sqrt{ 35} } }$

=>    $t =1.87$

Generally from the z table the p-value of  $(Z > 1.87 )$  is  

    $p-value = P(Z > 1.87) = 0.030742$