Test 2 | IEE 2610, Fall 2016 [18 points) The following problems are to be approa

Question

Test 2 | IEE 2610, Fall 2016 [18 points) The following problems are to be approached with the concepts of hypothesis testing. In answering each part of this question, identify: A complete hypothesis statement (i.e. Step 2 of hypothesis testing procedure), using appropriate parameters and values. • The required test statistic equation (equation only, eg. “Z, = XHA). • The required critical value reference (variable with proper subscripts only, e.g. "Za/2"). NOTE: You are NOT being asked to calculate the test statistic, nor are you being asked to perform the table lookup. table lookup.

Explanation / Answer

a)

H0 : p = 0.1 that is the proportion of defectives in the whole lot is 10%

H1 : p > 0.1 that is the proportion of defectives in the whole lot is greater than 10%

Test statistic: z = ( p – p0)/[p0(1-p0)/n] = (0.15-0.1)/ [0.1(1-0.1)/100]

Where p is the sample proportion

P0 is the hypothetical proportion

Critical value = z (it is one tail test) = z0.01

b)

H0 : µ = 1200

H1 : µ 1200

Test statistic : t = ( x - µ) / (s/n) = (1290-1200) / (110/10)

Critical value : t/2,n-1 = t0.025,9

c)

H0 : µmen = µwomen

H1: µmen µwomen

Test statistic: z = ( xmen - xwomen )/ [s2men / nmen + s2women / nwomen]

Critical value = z/2 = z0.025

d)

H0 : µ = 15

H1 : µ > 15

Test statistic : z = ( x - µ) / (s/n) = (17-15) / (3/36)

Critical value : z = z0.05

e)

H0 : 2 = 0.0002

H1 : 2 > 0.0002 (upper one tailed)

2 = (n-1)(s/o)2 = 9*(0.0003/0.0002)2

Critical value: 2(1-,n-1) = 2(1-0.15,9)

f)

H0 : 21 = 22

H1 : 21 22

F = s22 / s21 (since s22 is higher, it should be in the numerator)

Where s2 is the sample variance

Critical value = F/2,(n-1,n-1) = F/2,(5,5)

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