Is there evidence, at the 5% level of significance, to conclude that the floral scent improved the subjects' ability to complete the mazes?

The summary statistics are given on the Minitab output (you do not need to calculate the differences, or the mean and standard deviation of those difference), as well as a copy of the question from the textbook.

For each of the following assumptions, name the condition needed to check it ( if applicable) and explain, in the context of the problem, whether or not it is met.

Note that the normal population assumption, nearly normal condition is not met because the histogram of the differences in the time it took to complete the maze is not symmetric, so we need to check the sample size assumption.

1) Paired data assumption

2) Independence assumption (this is an experiment)

3) Sample size assumption

5) Define the parameter in the context of the problem

6) Calculate the text statistics, using the summary statistics given on the Minitab output. Show your work, but you do not need to include the formula

7) We used Minitab to get the p-value, which is 0.095. Briefly assess the significance of the evidence

8) Which of the following is the correct conclusion in the context of the problem?

a. since the assumptions are met, we have weak evidence to conclude at a 5% level of significance that the floral scent improves peoples' ability to complete the mazes (i.e scent has an effect), for this population model.

b. since the assumptions are met, we cannot conclude at a 5% level of significance that the floral scent improves peoples ability to complete the mazes (i.e. scent has an effect), for this population model.

c. Since the assumptions are met, we cannot conclude at a 5% level of significance that there is a difference in the mean time it takes to complete the maze between no scent and floral scent, for this population model.

d. since the assumptions are met, we have weak evidence that the floral scent improves peoples ability to complete the mazes (i.e.that scent has an effect) for this population model.

9) What type of error could you have made (Type 1 or Type 2) explain in context

10) Based on your conclusion in part e (question 8) which of the following is the correct range for a 95% confidence interval ? You do not need to calculate the interval

a. (-9.77,-2.07)

b. (-2.07,9.77)

c. (2.07, 9.77)

Minitab Output Descriptive Statistics: DIFF Statistics Variable N Mean SF Mean S:Dev Minimum Q1 Median Q3 Maximum DIFF 21 3.85 1301 18.80 800 3.80 15.20 22.50 Histogram of DIFF Histogram of DIFF 30 Percent 15 24 DIFF