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Math 533

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Brief Introduction:
AJ Davis is a department store chain, which has many credit customers and want to find out more information about these customers. AJ Davis has complied a sample of 50 credit customers with data selected in the following variables: Location, Income (in $1,000’s), Size (Number of people living in the household), Years (number of years the customer has lived in the current location), and Credit Balance (customers current credit card balance on the store’s credit car, in $).

The manager at AJ Davis has speculated the following: a. The average (mean) annual income was less than $50,000. b. The true population proportion of customers who live in an urban area exceeds 40% c. The average (mean) number of …show more content…

* My calculated test statistic of -2.07 falls in the rejection region of z < -0.1645, therefore, I would reject the null hypothesis and say there is sufficient evidence to indicate u<50 or $50,000.

b. The true population proportion of customers who live in an urban area exceeds 40%

* 22 of the 50 surveyed live in the Urban area, which is 44% or 0.44, this is the point estimate for p.

* Therefore my hypothesis would be * Ho: = 0.40 vs. Ha: p>0.40

* In order to conduct the large sample z-test, we first need to verify that the sample size is large enough. * nPo= 50(0.40) = 20 and 50 (1-0.44) = 30, both are larger than 15, so we can conclude that sample size is large enough to apply the large sample z test.

* Z= (0.44 – 0.400)/ 0.69282= 0.58 where s phat= sqrt (((0.40) (0.60))/50= 0.069282

* This is a one tailed (upper or right since HA has “>”). Our rejection regions would be z > 1.645.

* 0.58 is not greater than 1.645 (and is not in the rejection regions) so we would not Reject the Ho.

* The p-value= 0.282. The p-value is another complementary and equally valid way we can evaluate the null and alternative hypotheses is by looking at the p-value and compare the p-value to alpha. If the p-value is less than alpha, reject the null hypothesis and accept the alternative

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