Question

A prominent university conducted a survey on the effect of part-time work on student grade point average (GPA). Let x be the hours worked per week and y the GPA for the year. A summary of the results is below. What can the university conclude with α = 0.05?

n = 29

	y

= 69  

	x

= 517

	y2

= 189

,

	x2

= 11703

	yx

= 1392

,

	y − ŷ 2

= 14

a) Compute the quantities below.
₀ = ____, = _____
What GPA is predicted when a students works 6 hours a week?


b) Compute the appropriate test statistic(s) for H₁: β > 0.
Critical value = _____ ; Test statistic = _____
Decision:  ---Select--- (Reject H0 or Fail to reject H0)

c) Compute the corresponding effect size(s) and indicate magnitude(s).
If not appropriate, input and/or select "na" below.
Effect size =_____ ;   ---Select--- (na, trivial effect, small effect, medium effect, large effect)

d) Make an interpretation based on the results.

-More hours of part-time work significantly predicts a higher GPA.

or

-More hours of part-time work significantly predicts a lower GPA.    

or

-Part-time work does not significantly predict GPA.

Answer 1

(154 41 Wella: asdation siment unicorn cu skatted Required information is given hel EX: 511 ICY-DELU ty: 6 1 Ext. 11 to 3 Iy: 189 D: 29 ZYX - 1990 Calcoatet @ Compute the quantiters belowi- gilan quantitas below Valds are we have to obtained the (fere, B = Oxy - (2x = 0 nEx² Ex2 = @9* 1890]- (517*69] 09 x 11 703] – [51702 c1d368 – 035673 638387 - 964089] 41695 72098 Bi = 0.06517 and PRO = 2

a. - 6 - (0-06 5 X 1) - 69 - (3.666 29 05.363813 Bo = 121855 Therefore, Regression line TV : 1-21855+ 0.0651 Â - and also find out the Gper predicted value its Clere From Eg? ☺ I weget predicted value is W = 1.21855 +6.06511 * x] put (X= 6] ♡ = 1.21855+[0.06511 * 6] =121855 + 0.39066 ŷ = 160921 Therefore, predicted Kalce its 17.60927

O Compte the appiopriak: test (slavistics Cur baleto oblined the appio priate. test Glasicshic Kako is Efore, sal hypothesis is Ho i Bizo and. Alternative hypothesis is (He: Biso t-critical Calle as talz, d] -t10-05l2, df=239-2] =t0.025, 25] +xl, d)= 0.0518 tcriticas 0.052 + Cale is test statistic t-test = (SEERI] ī -@

where (ECB)-11 ✓ Ex-nox) Al lor (v) = I cyi-yJ? - 14 Da-1 = 161 08 20.5 0.5 CE CÊi) = lu toe-oa (542) 10.5 Vilto3 - Coax C17.827,2] 10.5 vito3 - 9016.86 0.5 v UB6.13 - 0.0111x104 (CECÊJ = 0.016118 0..0651 0.olul 8 It = 4.590) - test statistic compared the t-critical and todelst we have to Calce is)

H-Critical at kast 0.052 (1.590 -) we need there by pulbesis of 010.05 There for auce to ot :0.05 1 © copike Effenesite : coo hole to oblained the Effect size by casing given data is Chere, Effect size is, 2= ($xy) ² (iss xx xCSYY) cheie wsxy = EXY - Exzy = 1390 - C6qx 517) = 1322 - 230-10 CSS XY = 161.89 and Sxx = EX- EN = 11703 - 09732 = 11703 - 2016.86 SKY - JU86.137 Syy = Ey? = 189 - Coo = 189 - 184.17 Tisyy = 1.84

161.89 T2- Qu86.137*XI. 82) 161.89 61705.92 fre=0.00062 1 - and effect is [ALAJ Make IDterpretation: = we have to interpret the gives lakes is Gere - more bours of part-time Coork significantly predicts a locoer GpA Therefore, option ® its Correct answer