Question

Review pages 0.3 and 0.4 in the online notes if you are not familiar with using the equation editors in Word and Canvas.
1. Use the Word Equation Editor to complete the following formulas using the correct symbols here. [10 points]
   A. Sample standard deviation
s=
B. z score in a sample
z=

2. Go to the discussion board titled “Lab Question 2” and post the formulas for a sample standard deviation and for a z score in a sample using Canvas’ ’Insert Math Equation’. Take a screen capture of your discussion board post and copy + paste it here. Do not include a screen shot of your entire screen, just of your discussion board post. [10 points]

3. This question set will use the FisherIris.MTW dataset. These data were collected by Sir R. A. Fisher and published in a 1936 paper. There are five variables: type of iris, which is categorical; and, petal width, petal length, sepal width, and sepal length (all in millimeters), which are quantitative. [30 points; 5 points each]

A. Use Minitab Express to construct a histogram for the SepalWidth variable. Copy + paste your graph here.

B. Describe the shape of your distribution of sepal widths from part B. Use statistical terminology.

C. Use Minitab Express to compute the following descriptive statistics for the SepalWidth variable: mean, median, mode, standard deviation, and interquartile range. Copy + paste your output here as a PNG (right click > Copy As PNG).

D. Use Minitab Express to construct a dotplot for the PetalWidth variable. Copy + paste your graph here.

E. Describe the shape of your distribution of petal widths from part E. Use statistical terminology.

F. Use Minitab Express to construct a bar chart to display the data concerning type of iris (i.e., Type). Copy + paste your graph here.

3. This question set will use the USStates.MTW dataset. Remember to always include all relevant Minitab Express output and to always clearly identify your final answer. [50 points; 5 points each]

A. For the ObamaRomney variable, what proportion of states were for Romney (i.e., “R”)?

B. Use Minitab Express to take a simple random sample of 15 from the ObamaRomney variable. If you need a review of simple random sampling, see 1.2.2.1 of the online notes. Include a screenshot of your simple random sample here. Do not include a full screenshot, only your simple random sample.

C. In your simple random sample in part B, what proportion of states were Romney states?

D. Use Minitab Express to take a second simple random sample of 15 from the ObamaRomney variable. Include a screenshot of your simple random sample here.

E. In your second simple random sample in part D, what proportion of states were Romney states?

F. Use Minitab Express to take a third simple random sample of 15 from the ObamaRomney variable. Include a screenshot of your simple random sample here.

G. In your third simple random sample in part F, what proportion of states were Romney states?

H. Why were the proportions in the three simple random samples different from one another and different from the proportion in the population? You will need at least two sentences to completely answer this question.

I. Use Minitab Express to construct a two-way table for the ObamaRomney and Region variables. Copy + paste your output here as a PNG (right click > Copy As PNG).

J. What proportion of states in the South (i.e., Region=S) were Romney states?

Answer 1

Solution:-

1)

a) Sample standard deviation

$\sigma_{\bar{x}} = \sqrt{\frac{\sum \left ( x-\mu \right )^{2}}{(n-1)}}$

b) z score in a sample

$z = \frac{x-\mu }{\sigma }$