Statistics, Course Project Part B

Keller Graduate School of Management


Project Part B:

Answer
a. In this part of the project I am going to examination the managers claim that the average mean yearbook income was less than $50,000. The supposition examineing is done through the sideline steps:
The bootless hypothesis H0 is that the mean yearly income ? is get even to $50,000. H0:? = $50,000.
The alternative hypothesis H1 is that the mean annual income ? is less than $50,000. H1:? < $50,000
importation level chosen is 5% or ? = 0.05
Here, the population modular deviation is unknown. Hence, we use a t statistic Therefore the try statistic used is
t = X-?S/n follows a t distribution with n-1 degrees of freedom
From the t table agree to 0.05 opportunity, the critical take to be t? =1.6766. Hence the critical region is t < -1.6766. Alternatively, we baulk the fruitless hypothesis, if the p value is less than the conditional relation level
subbing the value we get
t = 43.74-5014.6396/50 = -3.02

The p value corresponding to t = -3.02 and 49 d.f. is 0.002 which is elfiner than the significance level.
The value of the test statistic is in the critical region and hence it is significant.



Therefore, we reject the null hypothesis at 5% level of significance.
The p-value is 0.002 which is smaller than the significance level. Hence there are 0.002 chances that such a small value can observe when the null hypothesis is true. Since, this probability is smaller than the significance level we reject the null hypothesis at 5% level.
Hence, we conclude that there is enough express to support the managers claim that the average annual income was less than $50,000.

b. The claim is that the true population proportion of customers who plump in an urban area exceeds 40%. In the given up sample of size 50, thirteen are from the Urban.
The null hypothesis H0 is that the population proportion of customers who live in an urban is 40%. H0:p = 0.40.
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