A large scale company claims that the average salary paid for their employees is

Question

A large scale company claims that the average salary paid for their employees is $50,000. A sample of 50 employees is surveyed and the details of their salaries are recorded. The sample mean of salaries is obtained as $44,025. Previous records show that the standard deviation of salary as $5000. At 10% level of significance do we have sufficient evidence to say that the average salary is less than the claim?

Null Hypothesis:   vs. Alternative Hypothesis

What tail test is this? (write only left, right, or two)

c) Find the Critical value (Table value): (it is recommended that you draw the appropriate distribution and illustrate the critical value, give answer to two decimal places)

d) Compute the test statistic: (give answer to four decimal places)

e) Obtain the p-value: (give answer to four decimal places)

f) Conclusion: (write only reject or fail to reject in all lower case)  

h) Using (p, a, z, c) to represent (p-value, alpha, test statistic, critical value) respectively write the statements that support your conclusion for each method: (answers should be inequalities) In other words what are the decision rules that support your conclusion?

P-value method:

Critical value method

Explanation / Answer

a)

As given,

n = 50
Xbar = 44025
alpha = 0.1
sigma = 5000 [ANSWER]

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b)

Formulating the null and alternative hypotheses,              
              
Ho:   u   >=   50000  
Ha:    u   <   50000  
              
As we can see, this is a    left   tailed test. [ANSWER]

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c)      
              
Thus, getting the critical z, as alpha =    0.1   ,      
alpha =    0.1          

Hence,

zcrit = -1.28 [ANSWER]

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d)
              
Getting the test statistic, as              
              
X = sample mean =    44025          
uo = hypothesized mean =    50000          
n = sample size =    50          
s = standard deviation =    5000          
              
Thus, z = (X - uo) * sqrt(n) / s =    -8.449926035 [ANSWER]

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f)          

As z < -1.28, we reject Ho. [ANSWER]

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g)

There is significant evidence that the true mean salary in the company is less than $50000.

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h)

P value method: As P < alpha, we reject Ho. There is significant evidence that the true mean salary in the company is less than $50000.

Critical value method: As z < -1.28, we reject Ho. There is significant evidence that the true mean salary in the company is less than $50000.

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