Question

Determine the appropriate critical value(s) for each of the following tests concerning the population mean: а.НА: μ > 1 1, n = 13, σ = 10.5, α = 0.05 b. HA: μ#22, n-24, s-34.52, α 0.02 c. HA: μ关30, n= 38, σ-34.524 α= 0.20 d. HA: μ <46; data: 13.4, 16.2, 42.9, 22.3, 18.8; α-o.10 e.HA : x > 14, n-24, σ-10.3

Answer 1

a)

Ho :   µ =   11
Ha :   µ >   11
      
Level of Significance ,    α =    0.05
population std dev ,    σ =    10.5
Sample Size ,   n =    13

SINCE SIGMA IS KNOWN, Z TEST WILL BE USED(one tail)
critical z value, z*   =   1.6449 [ excel formula , =NORMSINV(1-α) ]
B)

Level of Significance ,    α =    0.02
sample std dev ,    s =    34.52

Sample Size ,   n =    24  
degree of freedom=   DF=n-1=   23

since sigma is not known, t-test will be used(two tail)
critical t value, t*   = ± 2.4999
[EXCEL FORMULA =T.INV(α/2,DF) ]

c)SINCE SIGMA IS KNOWN, Z TEST WILL BE USED(two tail)

critical z value, z*   = ±1.2816

[ excel formula , =NORMSINV(α/2) ]

d)

since sigma is not known, t-test will be used(one tail)
here,n=5

degree of freedom=   DF=n-1=   4

critical t value, t*   =   -1.5332
[EXCEL FORMULA  =T.INV(α,df) ]

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