Strategics for business

Strategics for business
Decision

Table of Contents
Week 7: Question 2..........................................................................................................................1
a. Provide 95% confidence interval for all patients....................................................................1
b. Sample size required to estimate proportion of all hospitals..................................................1
Week 8: Question 10........................................................................................................................2
Hypothesis...................................................................................................................................2
Test statistic formula...................................................................................................................2
Level of significance...................................................................................................................2
Decision rule...............................................................................................................................2
Calculation..................................................................................................................................2
Conclusion...................................................................................................................................3
Week 9: Question 3..........................................................................................................................3
a. Null and alternative hypothesis...............................................................................................3
b. Decision rule ..........................................................................................................................3
c. Calculate the test statistic........................................................................................................3
d. Decision...................................................................................................................................5
Week 10: Question 2........................................................................................................................5
a. Estimated regression line and interpret the slope....................................................................5
b. Estimated total personal wealth when a person is 50 year old................................................5
c. What is value of coefficient of determination.........................................................................6
d. testing the value at 10% level of significance.........................................................................7
Week 11: Question 3........................................................................................................................8
a. Estimated regression equation.................................................................................................8
b. Compute the coefficient of determination...............................................................................9
c. Test to determine y is significantly related to independent variable.......................................9
d. Test whether x and y are significantly related......................................................................10

Week 7: Question 2
a. Provide 95% confidence interval for all patients
The proportion is as mention below:
Step 1:
CI = p +- Z(a/2) √p (1 – p) / n
in which P = sample proportion and n= sample size
So, as per the question n= 400 and the level of significance is 0.05 which is fixed.
Therefore, sample proportion = x / n
So, sample proportion = 800 / 400
= 0.2
Step 2:
In accordance with the table of standard normal distribution, there is a need to find the critical
value and the level of significance is 0.05 in which z= 1.96
so, = CI = p +- Z(a/2) √p (1 – p) / n
=0.2 +,- 1.96 √0.2 (1 – 0.2) / 400
= 0.2 +- 1.96 (0.02)
= 0.2 +- 0.0392
= (0.1608 and 0.2392)
b. Sample size required to estimate proportion of all hospitals
Confidence level 95%
Margin of error 4%
Population Proportion 50%
Sample size 601
So, it is interpreted that when 0.04% of margin of error is given, then the sample size estimated
for proportion of all hospitals referrals to the health care is 601.
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Week 8: Question 10
Hypothesis
H>0 Null Hypothesis: To determine there is no significant relationship between salaries and
population
H>1 Alternative hypothesis: To determine there is a significant relationship between salaries and
population
Test statistic formula
Z score = x- μ/ Standard deviation
Where x is raw score and is population mean.
Level of significance
The Z score value is 0.2 and on the other hand p value is 0.079 which is greater than 0.05 and
when the value if higher than level of significance which means alternative hypothesis is
accepted. So, it is reflected that there is a significant relationship between salaries and
population.
Decision rule
As per the decision rule, it is stated that if the test statistic follows a normal distribution
then critical value from the standard normal distribution which is known as Z statistic. So the
rule state that when the Z score value of greater than 0.05 then the alternative hypothesis is
accepted and on the other other side when the value is less than 0.05, if means the null
hypothesis is accepted while alternative hypothesis is rejected.
Calculation
Step 1: x- μ/ Standard deviation
Step 2: 50000-48400 / 8000
Step 3: 0.2
So, p-value from the Z table shows that
P (x<50000) = 0.57926
P(x>50000) = 1- P (x<50000) = 0.42075
P (48400 < x < 50000) = P (x< 50000) – 0.5 = 0.07926
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