# Statistics Assessment Homework Questions

Statistics Assessment Homework Questions

HW11

MGMT 07/31/2021

Chi Square

An analyst at a local bank wonders if the age distribution of customers coming for service at his branch in town is the same as at a branch located near the mall. He selects 100 transactions at random from each branch and researches the age information for the associated customer. These are the data :

Age

less than 30 30-55 56 or older Total

In town 20 40 40 100

mall 30 50 20 100

Total 50 90 60 200

1 What is the null hypothesis if you want to check if the age patterns of customers are independent of bank location?

2 What are the expected numbers for each cell in a 3 by 3 table if the null hypothesis is true?

3 Use the chi square test to accept or reject the null hypothesis. What is the chi square test statistic?

4 What is the chi square critical value and how many degrees of freedom does it have? Assume alpha is .05.

5 What do you conclude?

ANOVA

Saeko owns a yarn shop and want to expands her color selection.

Before she expands her colors, she wants to find out if her customers prefer one brand

over another brand. Specifically, she is interested in three different types of bison yarn.

As an experiment, she randomly selected 21 different days and recorded the sales of each brand.

At the .10 significance level, can she conclude that there is a difference in preference between the brands?

Misa’s Bison Yak-et-ty-Yaks Buffalo Yarns

799 776 799

784 640 931

807 822 794

675 856 920

795 616 731

875 893 837

Total 4,735.00 4,603.00 5,012.00

6) What is the null hypothesis?

What is the alternative hypothesis?

What is the level of significance?

7) Use Tools – Data Analysis – ANOVA:Single Factor

to find the F statistic:

8) From the ANOVA output: What is the F value?

What is the F critical value?

9) What is your decision?

Explain in statistical terms

Regression

Studies have shown that the frequency with which shoppers browse Internet retailers is related to the frequency with which they actually purchase products and/or services online. The following data show respondents age and answer to the question “How many minutes do you browse online retailers per year?”

Age (X) Time (Y)

16 307

17 285

19 267

22 343

22 393

22 287

22 253

28 364

28 251

28 248

28 433

30 319

33 226

34 321

35 336

35 302

35 476

36 395

39 473

39 342

40 539

42 455

43 326

44 565

48 385

50 590

50 507

51 333

52 426

54 261

58 625

59 252

60 615

10) Use Data > Data Analysis > Correlation to compute the correlation checking the Labels checkbox.

11) Use the Excel function =CORREL to compute the correlation. If answers for #1 and 2 do not agree, there is an error.

The strength of the correlation motivates further examination.

12) a) Insert Scatter (X, Y) plot linked to the data on this sheet with Age on the horizontal (X) axis.

b) Add to your chart: the chart name, vertical axis label, and horizontal axis label.

c) Complete the chart by adding Trendline and checking boxes

Read directly from the chart:

13) a) Intercept =

b) Slope =

c) R2 =

Perform Data > Data Analysis > Regression.

14) Highlight the Y-intercept with yellow. Highlight the X variable in blue. Highlight the R Square in orange

15) Use Excel to predict the number of minutes spent by a 22-year old shopper. Enter = followed by the regression formula.

Enter the intercept and slope into the formula by clicking on the cells in the regression output with the results.

16) Is it appropriate to use this data to predict the amount of time that a 9-year-old will be on the Internet?

If yes, what is the amount of time, if no, why?

Cleaning Data with Outlier

17) On this worksheet, make an XY scatter plot linked to the following data:

X Y

1.01 2.8482

1.48 4.2772

1.8 4.788

1.81 5.3757

1.07 2.5252

1.53 3.0906

1.46 4.3362

1.38 3.2016

1.77 4.3542

1.88 4.8692

1.32 3.8676

1.75 3.9375

1.94 5.7424

1.19 2.4752

1.31 26.2

1.56 4.5708

1.16 2.842

1.22 2.44

1.72 5.1256

1.45 4.3355

1.43 4.2471

1.19 3.5343

2 5.46

1.6 3.84

1.58 3.8552

18) Add trendline, regression equation and r squared to the plot.

Add this title. (“Scatterplot of X and Y Data”)

19) The scatterplot reveals a point outside the point pattern. Copy the data to a new location in the worksheet. You now have 2 sets of data.

Data that are more tha 1.5 IQR below Q1 or more than 1.5 IQR above Q3 are considered outliers and must be investigated.

It was determined that the outlying point resulted from data entry error. Remove the outlier in the copy of the data.

Make a new scatterplot linked to the cleaned data without the outlier, and add title (“Scatterplot without Outlier,”) trendline, and regression equation label.

X Y

1.01 2.8482

1.48 4.2772

1.8 4.788

1.81 5.3757

1.07 2.5252

1.53 3.0906

1.46 4.3362

1.38 3.2016

1.77 4.3542

1.88 4.8692

1.32 3.8676

1.75 3.9375

1.94 5.7424

1.19 2.4752

1.56 4.5708

1.16 2.842

1.22 2.44

1.72 5.1256

1.45 4.3355

1.43 4.2471

1.19 3.5343

2 5.46

1.6 3.84

1.58 3.8552

Compare the regression equations of the two plots. How did removal of the outlier affect the slope and R2? Explain why the slope and R Square change the way they did

20)

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Statistics Assessment Homework Questions