Compute the means of all possible samples of size and

Question

Data Analysis and Interpretation

1. Describe graphically the daily closing price and the value of the stock, Emaar Properties PJSC, During 01/01/2013 - 01/01/2015.

2. Find the five-Numbers Summary for the daily closing price and value for Emaar Properties PJSC, During 01/01/2013 - 01/01/2015.

3. Compute the μ, and σ for the daily closing price and value for Emaar Properties PJSC, During 01/01/2013 - 01/01/2015.

4. Discuss and give the sampling distribution of x' for a random sample of 25 daily closing prices selected from the given population. Assume the population is Normal.

i) Find the probability that x' will be less than 7.9 AED [P (x'<8.3 )]

ii) Find the probability that X will be less than 7.9 AED [P (X <8.3 )]

iii) Which result you trust more? explain

5. Use Excel or any statistical package to select 5 random samples of 20daily closing prices(simple random samples or systematic random samples), and findthe sample mean x' for each sample.

6. Calculate and interpret the mean, and standard deviation of the 5random sample means obtained in the previous question.

7. Select a simple random sample of size 5 for the daily closing price and consider it as a population. Consider all possible samples of size 2 from that population

i) Compute the means of all possible samples of size 2.

ii) Construct the sampling distribution of the sample means

iii) Compute the mean of all sample means μ_x and the variance of all sample means σ²x.

iv) Check your answer in questions iii) with

μx' = μ   σ²x = σ²/n

8. Construct and Interpreta 95% confidence interval for μ, the mean daily closing price for each of the 5 random samples selected in (5). Assume that the population is normally distributed with known σ as calculated in (3).Which confidence intervals contain the population mean μ of daily closing price obtained in (3)?

9. Repeat  (8) with a 90% confidence level. Comment on your findings.

10. Select a random sample of size 36 from the given population for the daily closing price and select another random sample of size 49 for the value in millions of AED.

i) At 5% significance level, Can you conclude that the population meanμ for the daily closing priceis different than 7.8 AED?

ii) Is there enough evidence to conclude that the true mean value of Emaar is more than 210 million AED. Use μ = 0.05

Attachment:- hypothesis testing.xlsx