9. A carpenter bought 4 rolls of electric wire. He got 60.24 meters of
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Linear programming which shows the best investment strategy for the client is Max Z=0.12I +0.09B and subject to constraints are :I+ B<=25000,
0.005 I +0.004B<=250.
Given maximum investment client can make is $55000, annual return= 9%, The investment advisor requires that at most $25,000 of the client's funds should be invested in the internet fund. The internet fund, which is the more risky of the two investment alternatives, has a risk rating of 5 per thousand dollars invested. the blue chip fund has a risk rating of 4 per thousand dollars invested.
We have to make a linear programming problem.
Let
I= Internet fund investment in thousands.
B=Blue chip fund investment in thousands.
Objective function:
Max Z=0.12I+0.09B
subject to following constraints:
Investment amount: I+ B<=25000
Risk Rating: 5/100* I+4/100*B<=250 or 0.005 I +0.004B<=250
I,B>=0.
Hence the objective function is Max Z=0.12 I+ 0.09 B.
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Answer:
If we compare the p value obtained and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.
Step-by-step explanation:
1) Data given and notation
n=500 represent the random sample taken
X represent the number of arrests that were not prosecuted.
estimated proportion of arrests that were not prosecuted
is the value that we want to test
represent the significance level
Confidence=98% or 0.98
z would represent the statistic (variable of interest)
represent the p value (variable of interest)
2) Concepts and formulas to use
We need to conduct a hypothesis in order to test the claim that the true proportion is less than 0.31.:
Null hypothesis:
Alternative hypothesis:
When we conduct a proportion test we need to use the z statisitc, and the is given by:
(1)
The One-Sample Proportion Test is used to assess whether a population proportion is significantly different from a hypothesized value
.
3) Calculate the statistic
Since we have all the info requires we can replace in formula (1) like this:
4) Statistical decision
It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.
The significance level provided . The next step would be calculate the p value for this test.
Since is a left tailed test the p value would be:
If we compare the p value obtained and the significance level given we have
so we can conclude that we have enough evidence to FAIL reject the null hypothesis, and we can said that at 2% of significance the proportion of arrests that were not prosecuted is not significanlty less than 0.31.