Answer:
From the question we are told that
The population mean is
The sample size is n = 30
The sample mean is
The population standard deviation is
The level of significance is
Step 1: State hypotheses:
The null hypothesis is
The alternative hypothesis is
Step 2: State the test statistic. Since we know the population standard deviation and the sample is large our test statistics is
=>
=>
Generally the degree of freedom is mathematically represented as
=>
=>
Step 3: State the critical region(s):
From the student t-distribution table the critical value corresponding to is
Generally the critical regions is mathematically represented as
Step 4: Conduct the experiment/study:
Generally the from the value obtained we see that the t value is outside the critical region so the decision is [Reject the null hypothesis ]
Step 5: Reach conclusions and state in English:
There is sufficient evidence to show that the filling weight has to be adjusted
Step 6: Calculate the p-value associated with this test. How does this the p-value support your conclusions in Step 5?
From the student t-distribution table the probability value to the right corresponding to at a degree of freedom of
is
Generally the p-value is mathematically represented as
=>
=>
Generally looking at the value obtained we see that hence
The decision rule is
Reject the null hypothesis
Step-by-step explanation: