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

Answer 1

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.

Answer:

Yes the true mean weight is less than 4 ounce

Explanation:

  From the question we are told that

     The random sample is $n = 15$

       The mean weight is $\= x = 3.8\ ounce$

        The standard deviation is  $\sigma = 0.5 \ ounce$

         The  level of significance is  $\alpha = 0.05$

       

So

   The  null hypothesis is  $H_o : \mu \ge 4$

     The alternative hypothesis is $H_a : \mu < 4$

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

            $t_{0.05} = 1.79$

This value is  obtained from  the critical value table

Generally the test statistics is mathematically represented as

                $Test \ Statistics (ST) = \frac{\= x - \mu }{\frac{\sigma}{\sqrt{n} } }$

           =>  $ST = \frac{3.8 -4 }{\frac{0.5}{\sqrt{20} } }$

                $ST = - 1.79$

So since ST is less than $t_{0.05}$  then the null hypothesis would be rejected and the alternative hypothesis would be accepted so

  Thus the true mean weight is less than 4