Question

Hammermill Premium Inkjet 24 lb. paper has a specified brightness of 106. The data are given below and may be found on Canvas in the Excel file named Brightness. 106.98 107.02 106.99 106.98 107.06 107.05 107.03 107.04 107.01 107.00 107.02 107.04 107.00 106.98 106.91 106.93 107.01 106.98 106.97 106.99 106.94 106.98 107.03 106.98 At α = .01, does this sample of 24 randomly chosen test sheets from a day's production run show that the mean brightness exceeds the specification? Follow and show the 7 steps for hypothesis testing. (8 points) Determine the p-value and interpret its meaning. (3 points) What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer. (3 points) Verify your results using Minitab by attaching or including the Minitab output. (2 points)

Answer 1

Result:

Hammermill Premium Inkjet 24 lb. paper has a specified brightness of 106. The data are given below and may be found on Canvas in the Excel file named Brightness. 106.98 107.02 106.99 106.98 107.06 107.05 107.03 107.04 107.01 107.00 107.02 107.04 107.00 106.98 106.91 106.93 107.01 106.98 106.97 106.99 106.94 106.98 107.03 106.98 At α = .01, does this sample of 24 randomly chosen test sheets from a day's production run show that the mean brightness exceeds the specification? Follow and show the 7 steps for hypothesis testing. (8 points)

Single sample t test

Ho: µ = 106   H₁: µ > 106

Upper tail test

Sample Size	24
Sample Mean	106.9967
Sample Standard Deviation	0.0373

=131.038             

Table value of t with 23 DF at 0.01 level =2.4999

Rejection Region: Reject Ho if t > 2.4999

Calculated t = 131.038 falls in the rejection region

The null hypothesis is rejected.

There is enough evidence to support the mean brightness exceeds the specification of 106.

Determine the p-value and interpret its meaning. (3 points)

P value =0.0000

What assumption must you make about the population distribution in order to conduct the test in part a? Is the assumption valid? Use and include an appropriate graph from Minitab. Write a couple of sentences supporting your answer. (3 points)

We assume the data come from normally distributed population.

The K_S test value 0.161, P= 0.106 which is > 0.05 level of significance. This shows that the data follows normal distribution.

Verify your results using Minitab by attaching or including the Minitab output. (2 points)

The MINITAB output results confirms the result we reported.