Question

1. A machine that puts corn flakes into boxes is adjusted to put an average of 15 ounces into each box, with a standard deviation of 0.25 ounce. The distribution of ounces per box has a normal distribution. If a random sample of 12 boxes had a sample standard deviation of 0.38 ounce, does this data support the claim that the standard deviation has increased and the machine needs to be adjusted. Use a 0.01 level of significance.

1. This problem is about (circle the correct one):

One population proportion                      Two population proportions        

One population mean                             Two populations means (Independent samples)

One population standard deviation        Two populations means (paired samples)

Two population standard deviations

2. State the null and alternate hypotheses.

3. What is the level of significance?

4. List the requirements and show the numbers or information given to meet each requirement.

5. Circle which of the following Statcrunch methods you would use to test the hypothesis stated in part (b).

Proportion Stats – One sample         Proportion Stats-Two samples

Variance Stats – One sample           Variance Stats – Two samples

T Stats - One sample                 T Stats-Two samples (Independent)

T Stats - Paired

6. Use StatCrunch to find the P-value and show details of determining if Ho is rejected or not.

Write the interpretation of the results of the hypothesis test.

Answer 1

a) One population standard deviation - One population because the problem is talking about a single population from which a sample is extracted to be analyzed. And we are concerned whether the standard deviation of the population has changed from observing the sample

a) Null Hypothesis or Ho: σ = 0.25

Alternate Hypothesis or HA: σ > 0.25

a) Level of significance as mentioned in the question is 0.01

a) To solve this we'll use the chi-squared tables. We'll need χ2=(n−1)*(s2/σ2)

Here n = number of elements in the sample which is 12

s is the sample standard deviation which is 0.38

σ is the population standard deviation which is 0.25

We'll need the degree of freedom to find the p-value which is given by n-1 = 20 - 1 = 19. We'll compare this value against the level of significance to determine whether to reject the null hypothesis or not.

P.S. - Answering only 4 sub-parts as per the guidelines. Also, all subparts were marked as "a."