Question

In: Statistics and Probability

Schadek Co. asked you to analyze their sales orders for the years 2018 and 2019 to...

Schadek Co. asked you to analyze their sales orders for the years 2018 and 2019 to see how well their sales force is working, and if they increased the sales orders or not. Use the data set in table. Sales orders of randomly selected customers (Schadek is a B2B co) are listed for 50 states.

STATE ORDER2019 ORDER2018
Alabama 536 559
Alaska 487 514
Arizona 499 523
Arkansas 554 562
California 499 498
Colorado 556 539
Connecticut 513 509
Delaware 476 501
Florida 471 498
Georgia 473 491
Hawaii 469 486
Idaho 517 543
Illinois 591 576
Indiana 475 499
Iowa 575 593
Kansas 563 577
Kentucky 563 550
Louisiana 546 564
Maine 453 506
Maryland 491 508
Massachusetts 509 511
Michigan 573 561
Minnesota 577 580
Mississippi 553 566
Missouri 579 577
Montana 516 539
Nebraska 569 562
Nevada 470 509
NewHampshire 511 520
NewJersey 497 499
NewMexico 529 551
NewYork 476 495
NorthCarolina 474 493
NorthDakota 561 592
Ohio 522 534
Oklahoma 547 567
Oregon 499 526
Pennsylvania 479 500
RhodeIsland 489 501
SouthCarolina 464 486
SouthDakota 562 577
Tennessee 567 562
Texas 465 493
Utah 545 575
Vermont 505 511
Virginia 495 510
Washington 508 527
WestVirginia 497 527
Wisconsin 575 584
Wyoming 551 547

1) At the 0.05 significance level, can you conclude the workforce is successful?

    1. State the hypothesis
    1. State the decision criteria
    1. Compute the test statistic
    2. Decision and managerial decision

Solutions

Expert Solution

Here we want to test whether the sales order increase from 2018 to 2019.

Since the data is paired and sample size is n= 50> 30;

paired t - test is used.

Let Xi be the sales orders in year 2019

Similarly let Yi be the sales orders in year 2018.

Let

di = Xi - Yi

di =  increase in the sales orders .

and be the average increase in the sales orders .

Hence the null hypothesis is given as

vs the alternative hypothesis will be

i.e mean sales order increase from 2018 to 2019.

Obtaining the difference di = Xi - Yi

Obtaining the mean and standard deviation of difference

= -14.14

= 210.98

Hence

The test statistic is given as

= -6.88357

Obtaining the critical value from the t-table

df = n-1

=49

level of significance

( The full table is given at the end of answer)

Decision rule:

Reject H0 if

i.e t (calculated ) > t (critical value)

Since  

We failed to reject the null hypothesis.

Hence there is not sufficient evidence to conclude that    mean sales order increase from 2018 to 2019.

At the 0.05 significance level the  workforce is not successful ,

The t -table

orchestra answered 2 years ago
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