question archive Suppose that we wish to test Ho : µ=50 versus Ha : µ> 50, where the population standard deviation is known to equal 10
Suppose that we wish to test Ho : µ=50 versus Ha : µ> 50, where the population standard deviation is known to equal 10
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Suppose that we wish to test Ho : µ=50 versus Ha : µ> 50, where the population standard deviation is known to equal 10. Also, suppose that a sample of 90 measurements randomly selected from the population has a mean equal to 55. a) Calculate the value of the test statistic z. b) By comparing z with the critical value, test Ho versus Ha at α=0.05. c) Calculate the p-value for testing Ho versus Ha. d) Use the p-value to test Ho versus Ha at α= 0.1 e) How much evidence is there that Ho : µ=50 is false and Ha : µ> 50 is true?
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Given the following data;
Population mean (µ)=50
Population standard deviation (σ)=10
Sample mean (X?) =50
Sample size (n) =90
a) Test statistics
z=( X?- µ)/ σ/√(n) =(55-50)=(10/√90)
z=4.7434
Level of significance (α) =0.05
b)Critical value =1.6449
Reject the Ho as the test statistic(4.7434) ≥critical value (1.6449)
c) The p value (right tail) at z = 4.74 34is; p value = 0.0000
d) Reject the Ho since p-value =0.0≤α0.05
Since p-value (0.0000) < α (0.05), we reject H0.
Since p-value (0.0000) < α (0.01), we reject H0.
e) 100% evidence that Ho : µ=50 is false and H1: µ>50 is true
We reject H0 at all the levels since p-value is less than all the significance levels
There is sufficient evidence to conclude that µ=50
