# calculations in descriptive statistics, homework help

**Question description**

USE THE HARVARD REFERENCING SYSTEM THROUGHOUT THE REPORT

Problem 1 (25 pts)

The cost of 14 models of digitals cameras at a camera specialty store during 2014 was as follows:

340 450 450 280 220 340 290 370 400 310 340 430 270 380

1. Compute mean, median, mode, first and third quartile.

2. Compute the variance, standard deviation, range, interquartile range, coefficient of variation, standard error of the mean and Z scores.

3. Determine whether or not there are outliers? Explain.

4. Determine whether or not the data are skewed? If so, how?

5. Based on the previous results what conclusions can you reach concerning the price of digital cameras at a camera specialty store during 2014.

6. Construct a 90%, 95%, 99% confidence interval for the population mean cost of digitals cameras.

7. Interpret the meaning of each interval.

8. What assumption do you need to make about the population of interest to construct the confidence intervals?

Problem 2 (15 pts)

Consider the sample data for plants A, B, C & D of the above company, which are

tabulated in table 1. Test whether the four means are equal at the 5% level of significance. Perform a test that will compare all 4 means at once. We are not interested in pair-wise comparisons at this stage. Please show all the steps in your calculations.

Table 1:

A B C D

333 328 320 333

332 329 321 321

320 323 322 329

326 327 325 330

328 330 326 328

325 331 328 325

323 332 329 333

321 320 330 331

334 324 331 327

322 323 332

320 334

329

330

328

331

330

Problem 3 (30 pts)

Read the article attached above (p. 221 – 225)

«Performance and duration differences between online and paper–pencil tests» and answer the questions below.

Part A.

1. Develop a 95% confidence interval using data from this study.

2. Perform a hypothesis testing using data from this study.

(show all the the appropriate steps).

3. Suggest another statistical technique(s) for the purpose of this study. Explain.

Part B.

For this study briefly describe how the researcher draw conclusions from a sample about a population. Try to be as analytic as possible and use the comments bellow.

1. Determine (or define) the independent variable(s).

2. Determine (or define) the dependent variable(s).

3. Determine (or define) qualitative and quantitative variable(s).

4. Determine (or define) the sample and the population.

5. Describe the statistical method(s) being used and define inferential statistics. Interpret the meaning of p-value.

## Tutor Answer

Hi hamidsabah, Please check the attached file for detail, let me know if you have any questions, thank you. Best, James,

1.

Mean= (340+450+450+280+220+340+290+370+400+310+340+430+270+380)/14

=347.86

Reorder the list from minimum to maximum:

220, 270,280,290,310,340,340,340,370,380,400,430,450,450

Since the number of element in the list in even, the median is the average of 7th and 8th element

Median = (340+340)/2 = 340

340 appears 3 times in the list and is the most frequent, thus

Mode = 340

The 1st quantile is the median of the first half of the ordered list

220, 270,280,290,310,340,340

1st quantile = 290

3rd quantile is the median of second half of the ordered list

340,370,380,400,430,450,450

3rdquantile = 400

2.

Variance = {(340-347.86)2+(450-347.86)2+(280-347.86)2+(220-347.86)2+(340-347.86)2+(290-347.86)2

+(370-347.86)2+(400-347.86)2+(310-347.86)2+(340-347.86)2+(430-347.86)2+(450-347.86)2+

(450-347.86)2}/(14-1)

=4910.440

Standard deviation = (variance)1/2 = 70.075

The range of a set of data is the difference between the highest and lowest elements in the set.

Range = 450-220 = 230

interquartile range is difference betw...

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