In the study of 200 people described above, the mean number of sheets used in a visit to the toilet was 7.5 with a standard deviation of 3.5. Calculate a 95% confidence interval to estimate the mean number of sheets used by all people. Show your working for this question and interpret the interval.
b. Of the 200 people sampled, 25 responded yes to the question ‘Do you buy recycled toilet paper?' Calculate a 95% confidence interval to estimate the proportion of all people who use recycled toilet paper. Show your working for this question and interpret the interval.
c. The weight of a typical roll of toilet paper is normally distributed with a mean of 227g and standard deviation of 10g. A standard pack of toilet paper contains 8 rolls. What is the probability that the total weight of the pack of rolls is less than 1.84kg? Show your working (including a diagram of the distribution) for this question.
Question 2
Research Question:
Is there a difference between the number of toilet rolls used per month for those who do buy recycled toilet paper and those who do not buy recycled toilet paper?
The output below shows a comparison between the number of rolls of toilet paper used per month for those who do and do not purchase recycled toilet paper. Use the following computer output to answer the research question above in the form of an appropriate hypothesis test.
Two-sample T for rolls
recycled N Mean StDev SE Mean
no 175 5.96 1.06 0.080
yes 25 5.195 0.965 0.19
Difference = mu (no) - mu (yes)
Estimate for difference: 0.764
T-Test of difference = 0 (vs not =): T-Value = ***
P-Value = *** DF = ***
Both use Pooled StDev = 1.0499
Hypothesis Test:
Question 3
Research Question:
Is there a difference between the costs of toilet paper at Foodmart and Supagro?
Descriptive Statistics: Foodmart, Supago, Difference
Variable N Mean SE Mean StDev
Foodmart 12 0.3292 0.0266 0.0920
Supago 12 0.2883 0.0168 0.0583
Difference 12 0.0408 0.0166 0.0574
Supermarket chains compete fiercely to have the best products at the lowest prices. Data were collected on the price (in $) per 100 sheets of toilet paper for the same 12 brands at two chains Foodmart and Supagro. Minitab summaries of the data are given above. Use these summaries with an appropriate hypothesis test to determine whether the or not there is a difference in prices as per the research question.