Question

1. Calculate the median, the mode, the first quartile, and the average of your first series data. (5 mark)
2. Calculate the range, the variance and the standard deviation of your first data series. (5 mark)
3. What is the coefficient of variation and correlations of the two data series? (5 mark)
4. Construct a 95% confidence interval for the population mean of the random varible based on the first data series, assuming that you already know the variance value b. Interpret the confidence interval that you have contructed.
5. Continue with question 8d, how large a sample size is required for the margin of error for a 95% confidence interval width be a small as 0.25? ( 5 marks)
6. Construct a 95% confidence interval for the population mean of the random varible based on the second data series, assuming that you do not know the variance of the random variable. Interpret the confidence interval that you have contructed.
7. Conduct a hypothesis test that the population average is (c + 1) using the second series of data in the using both the critical value rule and p-value approach ? The test significance level is 5%. ( Please clearly lay out the steps of the test) ( 10 marks)
8. What is type II error of your test in 8g when the true mean is the known value of c? ( 10 marks)
9. Can you explain how sample size could affect hypothesis test result? ( 5 marks)
10. Conduct a hypothesis test that the population mean difference between the two series of data is zero. ( 10 marks)

Series I	Series II
1.72	7.03
1.81	6.94
1.93	7.02
1.96	6.89
1.96	7.06
2.00	6.97
2.06	6.95
2.07	6.98
2.13	6.98
2.16	7.04

Answer 1

a) In the first data series we have n= 10 values.

Median = middlemost value=(n+1)/2th value= 5.5th value = (1.96+2)/2= 1.98

Mode= value with highest frequency = 1.96 (occurs twice and others all occur once)

First Quartile= (n+1)/4th observation = 2.75th observation = 1.81*0.25 + 1.93*0.75= 1.9

Average or mean= (sum of all observations)/n = 1.98

b) Range= Highest value- lowest value= 2.16-1.72= 0.44

Variance = ()^2/n-1 = 0.018844

Standard deviation = √Variance= 0.13728

c) Coefficient of Variation = R^2

Correlation coefficient = R

R= Sxy/√(Sxx*Syy)

Sxy=

Sxx=

Syy=

Taking series 1 values as x and series 2 values as y,

From above we get, R= 0.00311 (correlation coefficient)

So R^2= 9.65*10^-6

d) 95% CI for the population mean is given as:

Sample mean +- z0.025*Sd/√n

= 1.98 +- 1.96*0.13728/√10

= (1.895, 2.065)