The Port Authority sells a wide variety of cables and adapters for electronic eq

Question

The Port Authority sells a wide variety of cables and adapters for electronic equipment online. Last year the mean value of orders placed with Port Authority was $47.28 and management wants to assess whether the mean value of orders placed to date this year is the same as last year. A sample of 100 orders placed this year collected and recorded below.

a)      At the 5% level of significance, test whether the mean value of this year’s orders differs from last year’s mean orders.

b)      Port Authority also wants to determine if the gender profile of its customers has changed from last year when 65% of orders were placed by male customers. Test at 5% level.

c)      At the 5% level of significance, can we conclude that the mean value of orders by male customers is higher than the mean value of orders made by female customers?

Order Value of Order Gender 1 $17.26 MALE 2 $58.76 MALE 3 $19.01 MALE 4 $46.86 MALE 5 $75.84 MALE 6 $54.20 FEMALE 7 $35.85 FEMALE 8 $61.59 MALE 9 $59.51 MALE 10 $40.11 MALE 11 $21.37 FEMALE 12 $54.78 MALE 13 $57.04 MALE 14 $41.09 FEMALE 15 $29.14 FEMALE 16 $74.29 MALE 17 $48.51 MALE 18 $65.84 MALE 19 $31.62 MALE 20 $37.40 FEMALE 21 $39.09 MALE 22 $58.27 FEMALE 23 $62.63 FEMALE 24 $20.47 FEMALE 25 $67.27 MALE 26 $32.25 FEMALE 27 $43.21 FEMALE 28 $27.64 FEMALE 29 $60.65 FEMALE 30 $77.16 FEMALE 31 $64.87 FEMALE 32 $22.39 MALE 33 $32.26 MALE 34 $48.00 MALE 35 $40.90 MALE 36 $31.19 MALE 37 $76.01 MALE 38 $65.78 FEMALE 39 $23.11 FEMALE 40 $17.65 MALE 41 $42.77 MALE 42 $73.19 MALE 43 $75.00 MALE 44 $62.06 MALE 45 $41.67 MALE 46 $26.63 MALE 47 $29.68 FEMALE 48 $61.87 MALE 49 $31.11 FEMALE 50 $75.27 MALE 51 $17.10 MALE 52 $41.33 FEMALE 53 $25.58 FEMALE 54 $27.25 MALE 55 $58.17 FEMALE 56 $27.57 MALE 57 $59.16 MALE 58 $26.15 FEMALE 59 $52.99 MALE 60 $52.26 FEMALE 61 $39.12 MALE 62 $40.18 MALE 63 $26.19 MALE 64 $36.99 MALE 65 $62.26 FEMALE 66 $61.49 FEMALE 67 $51.22 FEMALE 68 $57.74 MALE 69 $30.03 MALE 70 $19.83 MALE 71 $49.71 FEMALE 72 $18.01 MALE 73 $43.11 FEMALE 74 $46.81 MALE 75 $21.23 MALE 76 $19.15 MALE 77 $79.25 MALE 78 $30.59 MALE 79 $51.21 FEMALE 80 $76.83 FEMALE 81 $78.26 FEMALE 82 $33.02 MALE 83 $75.48 MALE 84 $28.12 MALE 85 $22.36 FEMALE 86 $17.28 MALE 87 $67.01 MALE 88 $65.18 FEMALE 89 $42.58 MALE 90 $31.93 MALE 91 $43.54 MALE 92 $53.65 MALE 93 $70.84 MALE 94 $49.19 MALE 95 $23.55 FEMALE 96 $20.32 FEMALE 97 $53.03 MALE 98 $46.87 FEMALE 99 $47.01 MALE 100 $44.60 FEMALE

Explanation / Answer

a)

ho: mean value of this year’s orders differs from last year’s mean orders. U=47.28

h1: mean value of this year’s orders differs from last year’s mean orders. U=47.28

Xbar $45.22 AVERAGE(B2:B101)

sd 18.25349422 STDEV(B2:B101)

n 100 COUNT(B2:B101)

z = (X-mean)/(sd/sqrt(n))

=(45.22-47.28)/(18.25/SQRT(100))

-1.128767123

p-value

=2*(1-NORMSDIST(1.12877))

0.258994871

since p-value > 0.05, I fial to reject ho and conclude that

mean value of this year’s orders differs from last year’s mean orders. U=47.28

b)

ho: 65% of orders are placed by male customers. P=.65

h1: 65% of orders are NOT placed by male customers. P =/= .65

X= 62 AVERAGE(B2:B101)

n= 100 STDEV(B2:B101)

p-hat= X/n= 0.62 COUNT(B2:B101)

z = (phat-po)/sqrt(po*(1-po)/n)

=(0.62-0.65)/SQRT(0.65*(1-0.65)/100)

-0.628970902

p-value

=2*(1-NORMSDIST(0.62897))

0.529368697

since p-value > 0.05, I fial to reject ho and conclude that

65% of orders are placed by male customers. P=.65

c)

ho: mean value of orders by male customers is equal to the mean value of orders made by female customers

h1: mean value of orders by male customers is higher than the mean value of orders made by female customers

sd^2/n 5.71 8.09

df= =(5.71+8.09)^2/(5.71^2/61+8.09^2/37)

82.67918019

83

t= =(45.26-45.17)/SQRT(5.71+8.09)

0.024227186

p-value

P(T>t)

=T.DIST.2T(0.024227,83)

0.980729694

since p-value > 0.05, I fial to reject ho and conclude that

mean value of orders by male customers is equal to the mean value of orders made by female customers

male female mean $45.26 $45.17 AVERAGE sd 18.82 17.53 STDEV n 62 38 COUNT sd^2/n 5.71 8.09

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