Question

The daily returns for a stock over a period of 110 days are recorded, and the summary descriptive statistics are given as follows:

Descriptive Statistics: return

Variable	N	N*	Mean	SE Mean	StDev	Minimum	Q1	Median	Q3	Maximum
Return	110	0	0.000983	.00296	.03103	-.19992	-.01393	.00322	.01591	.09771

a) Find a 95% confidence interval estimate for μ, where μ is the population mean rate of return of the stock.

b) Test the hypothesis Ho:μ= 0 versus Ha:μ > 0 at 5% significance level.

What is the p-value for the test

Answer 1

Given,

Sample size : n = 110

Sample mean : = 0.000983

Sample standard deviation : s= 0.03103

Confidence interval estimate for , where is the population mean when population standard deviation is not known

for 95% confidence level = (100-95)/100 =0.05

/2 = 0.05/2 =0.025

degrees of freedom = n-1 =110-1=109

t_/2,n-1 = t_0.025,109 = 1.982

95% confidence interval estimate for , where is the population mean rate of return of the stock

95% confidence interval estimate for , where is the population mean rate of return of the stock = (-0.00488372 ,0.00684972 )

b)

Ho:μ= 0 versus Ha:μ > 0

Right tailed test

For Right tailed test:

For 109 degrees of freed, P(T>0.3321) = 0.3702

p-value = P(t>0.3321) =0.3702

p-value = 0.3702

As P-Value i.e. is greater than Level of significance i.e (P-value:0.3702 > 0.05:Level of significance); Fail to Reject Null Hypothesis