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Ec 351 Park

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Submitted By scdb89
Words 392
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Week 7 Homework
24.
H0: μ2 ≤ μ1
H1: μ2 > μ1

a = 0.05 (one-tailed)

z-crit = 1.645

test statistic z = (μ2-μ1) / √[(s1)²/n + (s2)²/m] = (351-345) / √[28²/60 + 21²/54] = 1.3

Failed reject H0 because 1.3 < 1.645 and conclude that the difference in means is not significant because the number of units produced on the afternoon shift is larger.

34.
These are independent samples of sufficient size to use the z-test for proportions.

n1 = 270 x1 = 56 n2 = 203 x2 = 52 α = 0.05

p1’ = x1/n1 = 56 / 270 = 0.2074

p2’ = x2/n2 = 52 / 203 = 0.2562

pbar = (x1 + x2) / (n1 + n2) = (56 + 52) / (270 + 203) = 0.2283

qbar = 1 – pbar = 1 – 0.2283 = 0.7717

H0: p1 = p2
Ha: p1 ≠ p2 (claim)

At α = 0.05 for a two-tailed test, zcrit = ±1.96

ztest = [ (p1’ – p2’) – (p1 – p2) ] / √[(pbar)(qbar)(1/n1 + 1/n2)] ztest = [ (0.2074 – 0.2562) – 0 ] / √[(0.2283)(0.7717)(1/270 + 1/203)] ztest = -1.2515
Since ztest > zcrit, the null hypothesis cannot be rejected.
There isn’t enough evidence to support the claim that there is a difference in the proportion of humorous advertisements in British vs American trade magazines.
37.
H0: μ2 ≤ μ1
H1: μ2 > μ1
Mean (1)=125.125 Mean(2)= 117.714
Sd(1)= 15.094 Sd(2)= 19.914

Sp2= 305.708 t= (125.125-117.714) / √[305.708 (1/8+1/7)] = 0.819
There is no difference in the mean number sold at regular price and the mean number sold at the reduce price. Therefore, we cannot reject the H0.

38. This is a one-tailed test. The critical value of t (from t table with 7 degrees of freedom) with .01 significance is 2.998

H0: dbar = 0
HA: dbar not = 0

Mean of differences -2.5
Standard deviation of differences = 2.9277
Standard error of difference-mean = sd / √ n
SE = 2.9277002 / 2.8284271
Standard error of difference-mean 1.0350983

t = dbar /se t = -2.5 / 1.035098 t = -2.4152

Because it

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