x -0.589195516 -1.165999365 -1.196664499 -1.257563483 -0.525990202 0.854812885 -0.793681837 -1.417444643 -0.587108308 -0.858825728 -0.701407141 -1.422989542 0.599696525 -1.284589636 -1.001937874...

x
-0.589195516
-1.165999365
-1.196664499
-1.257563483
-0.525990202
0.854812885
-0.793681837
-1.417444643
-0.587108308
-0.858825728
-0.701407141
-1.422989542
0.599696525
-1.284589636
-1.001937874
1.574345517
0.730310215
2.029936558
-1.478076688
1.275062193
-0.942099275
-0.46061074
-0.62507241
0.809409717
0.580538491
0.251508471
-1.450185083
-0.420038255
-0.689961171
-1.72796119
-0.354833098
-0.497321833
-0.931842764
0.893137646
-2.188091533
0.298304744
-1.747708258
0.646016624
-1.049316086
-1.803465357
-2.422502716
-1.228232298
-0.614929299
1.567587658
-1.657856428
-2.7386634
0.113007418
-0.951697983
0.168638923
-1.428134815
-0.961604508
1.40144609
-1.867649237
-0.590937753
-2.349109391
-0.681025494
0.969805116
-0.480300729
-1.069314969
-1.541400077
-1.317558745
-1.453097913
-2.554767597
-0.476209949
-1.61570377
-1.667946599
-3.104456395
-2.774839492
-0.64262904
-0.773472382
-1.326306176
1.652826435
-1.210134763
-1.95406961
-0.757037593
-3.255885219
-0.709987598
-0.600542346
0.257265473
-0.810623263
-1.468675022
-1.594713859
-1.305846467
-2.757993583
-1.127033746
-1.155410731
-1.991017298
-1.387325175
-1.418131527
-1.041117131
-1.767653169
-1.844893202
-0.868432167
-1.225046223
-0.984621442
-2.12815852
0.555438263
-1.652361438
-0.647983026
-1.07128309
0.727463182
-0.208681215
0.294125
0.466751148
2.30286538
-1.476263347
-1.096302138
-1.299764457
-3.14329683
-2.184234274
-0.251110181
-1.927897831
-0.929039859
-2.31559721
-0.129963556
-1.19765265
0.246344488
-1.919996909

There are 118 values that show the differences in productivity of workers measured before and after they undertake a training program.

Test the null hypothesis that the training program makes no difference to productivity against a two-sided alternative hypothesis using a significance level of 5%. In your answer, you should state the null and alternative hypotheses, the significance level, the PDF of the test statistic under the null hypothesis, the value of the test statistic, and your conclusion.
Do you need to make any assumptions in order for your test to be valid?

Expert Solution

The null hypothesis is: There is no difference in productivity pre and post training program

The alternate hypothesis is: There is difference in productivity pre and post training program

The level of significance is 5%

Since, the difference figures are provided, use t-test.

Had the pre & post figures were provided, paired t test would have been used.

The test result is:

The degree of freedom = n-1 = 117

At 5% level of significance, the critical t-statistic for two-tailed is given as 1.96

Since, the critical t-statistic is less than actual t-statistic of 8.32968 at 5% level of significance and at 117 degree of freedom, the null hypothesis is rejected.

This implies, there is statistically significant difference between pre and post training program on productivity.

The assumption that is made is that the series of values showing productivity is continuous & normally distribution.

Rahul Sunny answered 1 year ago

Let A = {x|x ∈ N∧x < 15}, B = {x|x ∈ Z∧x < 20∧x >...

Let A = {x|x ∈ N∧x < 15}, B = {x|x ∈ Z∧x < 20∧x > −4∧x/2 ∈ Z}, C = {x|x ∈ N∧x2 ∈ A}. Calculate the following expressions using the counting tools we have learned as appropriate. Show your work. |A ∪ B ∪ C| |A × (B ∪ C)| |A − B| + |C − B| + |B| − |(A ∩ C) − B|

AND( OR(OR(X,Y), AND(OR(X,Y), OR(NOT(X), NOT(Y)))), OR(OR(X,Y), AND(OR(X,Y), NAND(X,Y))) ) is equivalent to: A. OR(X,Y) B. AND(X,Y)...

AND( OR(OR(X,Y), AND(OR(X,Y), OR(NOT(X), NOT(Y)))), OR(OR(X,Y), AND(OR(X,Y), NAND(X,Y))) ) is equivalent to: A. OR(X,Y) B. AND(X,Y) C. NOR(X,Y) D. XOR(X,Y) E. NAND(X,Y) F. XNOR(X,Y) How do I simplify this with the Idempotence, De morgan, absorbtion law, etc and waht are the steps to break it down?

Evaluate lim x approaches 0+ x^x^x

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}....

Let X, Y ⊂ Z and x, y ∈ Z Let A = (X\{x}) ∪ {x}. a) Prove or disprove: A ⊆ X b) Prove or disprove: X ⊆ A c) Prove or disprove: P(X ∪ Y ) ⊆ P(X) ∪ P(Y ) ∪ P(X ∩ Y ) d) Prove or disprove: P(X) ∪ P(Y ) ∪ P(X ∩ Y ) ⊆ P(X ∪ Y )

Do the polynomials x^3 + x + 2, x^2 - x +2, -x^3 + x^2 -...

Do the polynomials x^3 + x + 2, x^2 - x +2, -x^3 + x^2 - 5x + 3, and x^3 + 2 span P3? (show your conclusion.)

x=0 x=2.5 x=5 x=7.5 x=10 x=12.5 pA tAx R(x) Land Rent(x) = Revenue(x)/unit area - Transport...

x=0 x=2.5 x=5 x=7.5 x=10 x=12.5 pA tAx R(x) Land Rent(x) = Revenue(x)/unit area - Transport Costs(x)/unit area or R(x) = pA - tAx for all farmed locations. Assume that in the base case p = 10, A = 100, and t = 2. Use the table to calculate R(x) a) Draw rent as a function of distance from the central railyard. b) What is the land rent at x = 12.5? Explain. c) Suppose that the price of apples...

Let P(x),Q(x),R(x), and S(x) be the statements “x is a duck,” “x is one of my...

Let P(x),Q(x),R(x), and S(x) be the statements “x is a duck,” “x is one of my poultry,” “x is an oﬃcer,” and “x is willing to waltz,” respectively. Express each of these statements using quantiﬁers, logical connectives, and the relations P(x),Q(x),R(x), and S(x). (a) No ducks are willing to waltz (b) No oﬃcers ever decline to waltz (c) All my poultry are ducks (d) My poultry are not oﬃcers (e) Does the fourth item follow from the ﬁrst three taken...

f(x)=0 if x≤0, f(x)=x^a if x>0 For what a is f continuous at x = 0...

f(x)=0 if x≤0, f(x)=x^a if x>0 For what a is f continuous at x = 0 For what a is f differentiable at x = 0 For what a is f twice differentiable at x = 0

a) y''(x)-3y'(x)=8e3x+4sinx b) y''(x)+y'(x)+y(x)=0 c) y(iv)(x)+2y''(x)+y(x)=0

Let f(x) = x - R/x and g(x) = Rx - 1/x a) Derive a Newton...

Let f(x) = x - R/x and g(x) = Rx - 1/x a) Derive a Newton iteration formula for finding a root of f(x) that does not involve 1/xn. To which value does the Newton iterates xn converge? b) Derive a Newton iteration formula for finding a root of g(x) that does not involve 1/xn. To which value does the Newton iterates xn converge?

Question