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
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