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# TASK DUE XXXXXXXXXX Question 01 A local health centre noted that in a sample of 400 patients, 80 were referred to them by the local hospital. a. Provide a 95% confidence interval for all the patients...

Question 01
A local health centre noted that in a sample of 400 patients, 80 were refe
ed to them by the local
hospital.
a. Provide a 95% confidence interval for all the patients who are refe
ed to the health centre by the hospital.
. What sample size would be required to estimate the proportion of all hospital refe
als to the health centre with a margin of e
or of 0.04 or less at 95% confidence?
Question 02
The average starting salary of students who graduated from colleges of Business in 2009 was \$48,400. A sample of 100 graduates of 2010 showed an average starting salary of \$50,000. Assume the standard deviation of the population is known to be \$8000. We want to determine whether or not there has been a significant increase in the starting salaries.
Step 1. Statement of the hypothesis
Step 2. Standardised test statistic formula
Step 3. State the level of significance
Step 4. Decision Rule (Draw a bell to show rejection zone)
Step 5. Calculation of the statistic
Step 6. Conclusion
Question 03
The data in the table below presents the hourly quantity of production for three lines of production processes over the first 4 days in XYZ Company. Answer the questions based on the Excel Output given below.
a. State the null and alternative hypothesis for single factor ANOVA.
. State the decision rule (Î± = 0.05).
c. Calculate the test statistic.
d. Make a decision.
Question 04
Personal wealth tends to increase with age as older individuals have had more opportunities to earn and invest than younger individuals. The following data were obtained from a random sample of eight individuals and records their total wealth (Y) and their cu
ent age (X).
a. State the estimated regression line and interpret the slope coefficient.
. What is the estimated total personal wealth when a person is 50 years old?
c. What is the value of the coefficient of determination? Interpret it.
d. Test whether there is a significant relationship between wealth and age at the 10% significance level. Perform the test using the following six steps.
Step 1. Statement of the hypotheses
Step 2. Standardised test statistic
Step 3. Level of significance
Step 4. Decision Rule
Step 5. Calculation of test statistic
Step 6. Conclusion
Question 05
A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained.
a. Write out the estimated regression equation for the relationship between the variables.
. Compute coefficient of determination. What can you say about the strength of this relationship?
c. Ca
y out a test to determine whether y is significantly related to the independent variables.
Use a 5% level of significance.
d. Ca
y out a test to see if x3 and y are significantly related. Use a 5% level of significance.
Answered Same Day Jun 14, 2021

## Solution

Biswajit answered on Jun 15 2021
Question 01
A local health centre noted that in a sample of 400 patients, 80 were refe
ed to them by the local
hospital.
a. Provide a 95% confidence interval for all the patients who are refe
ed to the health centre by the hospital.
Ans: p =80/400=0.2, standard deviation =sqrt (0.2 *(1-0.8)/400) =0.02, z @ 95% confidence interval =1.96
So, 95 % confidence interval (64.32,95.68) & if we round it then it is (64,96)
. What sample size would be required to estimate the proportion of all hospital refe
als to the health centre with a margin of e
or of 0.04 or less at 95% confidence?
Ans: Margin of e
or = Z @95% x Standard deviation = 1.96 *sqrt (0.2*0.8/n) <=.04
So, sample size (n) >= 384.16
Question 02
The average starting salary of students who graduated from colleges of Business in 2009 was \$48,400. A sample of 100 graduates of 2010 showed an average starting salary of \$50,000. Assume the standard deviation of the population is known to be \$8000. We want to determine whether or not there has been a significant increase in the starting salaries.
Step 1. Statement of the hypothesis
Ans: Null Hypothesis: Average starting salary of students who graduated from colleges of business = \$ 48,400
Alternate Hypothesis: Average starting salary of students who graduated from colleges of business > \$ 48,400
Step 2. Standardised test statistic formula
Ans: z statistic = (50,000-48,400)/ (8000/sqrt (100)) =2 as population standard deviation is given
Step 3. State the level of significance
Ans: .05
Step 4. Decision Rule (Draw a bell to show rejection zone)
Ans: If p value < 0.05 then reject null hypothesis or if calculated z statistic is greater than z critical then reject null hypothesis
Step 5. Calculation of the statistic
Ans: p value 0.023 or z critical is 1.645
Step 6. Conclusion
Ans: So as p (.023) calculated is less than level of significance (.05) then...
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