The weights of soy patties sold by a diner are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of​ significance

Complete Question

The weights of soy patties sold by a diner are normally distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a sample standard deviation of 0.5 ounces. At the 0.05 level of significance,perform a hypothesis test to see if the true mean weight is  less than 4 ounce.

Yes the true mean weight is less than 4 ounce

Explanation:

  From the question we are told that

     The random sample is

       The mean weight is

        The standard deviation is  

         The  level of significance is  

So

   The  null hypothesis is  

     The alternative hypothesis is

Generally the critical value which a bench mark to ascertain whether the null hypothesis is  true or false is mathematically represented as

This value is  obtained from  the critical value table

Generally the test statistics is mathematically represented as

           =>  

So since ST is less than  then the null hypothesis would be rejected and the alternative hypothesis would be accepted so

  Thus the true mean weight is less than 4