Question

In: Economics

You work for a candy company and the manufacturing manager claims that the production line produces...

You work for a candy company and the manufacturing manager claims that the production line produces bags of candy with an average of exactly 50 candies per bag.  

You are skeptical about this and you decide to test the claim by counting the candies in a sample of 25 bags.

You discover in your sample that x = 48and s = 5.

Determine whether or not you have enough statistical evidence to reject the manager's claim with a significance level of .05.

In order to get full credit you need to include the following seven items in your answer. Circle each of these answers.

  1. State the null and alternative hypotheses using mathematical symbols.
  2. Give the symbol for the test statistic you will use to test your hypothesis.
  3. Give the value of the test statistic.
  4. Calculate the number of degrees of freedom if necessary.
  5. Provide a range for the p-value (if you are using a table). You can also give the exact p-value if you are using a computer to calculate the answer.
  6. Give a statistical result for your hypothesis test (Reject or Fail to Reject) and include a note explaining why that is the right conclusion.
  7. Provide a sentence explaining your result in plain English with no statistical jargon.

Solutions

Expert Solution

(a) The Hypothesis

H0: = 50

Ha: 50

(b Since the population standard deviation is obscure and n < 30, we use the students t tesT

(c) The Test Statistic: The test statistic is given by the equation:

(d) The degrees of FREEDOM when using the t distribution is given byn - 1 = 25 - 1 = 24

___

(e) The p value ( 2 tail) = 0.0285

The t critical at = 0.05 is -2.064 and +2.064

(f) The Decision Rule:   If t observed is > t critical or If t observed is < -t critical, Then reject H0.

Also if P value is < , Then Reject H0.

The Decision: Since t observed (-2) falls in between -2.064 and +2.064, We Fail to Reject H0.

Also since P value (0.0285) is > (0.05) , We Fail to Reject H0.

(g) The Conclusion: There isn't sufficient proof to discredit the manufacturing managers claim that the production line produces bags of candy with an average of exactly 50 candies for each bag.

PLZ LIKE MY ANS

Rahul Sunny answered 2 years ago
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