In: Statistics and Probability
The average daily volume of a computer stock in 2011 was μ equals = 35.1 million shares, according to a reliable source. A stock analyst believes that the stock volume in 2014 is different from the 2011 level. Based on a random sample of 40 trading days in 2014, he finds the sample mean to be 25.5 million shares, with a standard deviation of s= 15.2 million shares. Test the hypotheses by constructing a 95% confidence interval. Complete parts (a) through (c) below.
B.) Construct a 95% confidence interval about the sample mean of stocks traded in 2014. The lower bound is ____ million shares.
The upper bound is _____ million shares.
C.)Will the researcher reject the null hypothesis?
A. Reject the null hypothesis because μ = 35.1 million shares falls in the confidence interval.
B. Do not reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.
C. Do not reject the null hypothesis because u=35.1 million shares falls in the confidence interval.
D. Reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.
b)
sample std dev , s = 15.2000
Sample Size , n = 40
Sample Mean, x̅ = 25.5000
Level of Significance , α =
0.05
degree of freedom= DF=n-1= 39
't value=' tα/2= 2.0227 [Excel
formula =t.inv(α/2,df) ]
Standard Error , SE = s/√n = 15.200 /
√ 40 = 2.4033
margin of error , E=t*SE = 2.0227
* 2.403 = 4.861
confidence interval is
Interval Lower Limit = x̅ - E = 25.50
- 4.861 = 20.6388
Interval Upper Limit = x̅ + E = 25.50
- 4.861 = 30.3612
95% confidence interval is (
20.64 < µ < 30.36
)
c)
Ho : µ = 35.1
Ha : µ ╪ 35.1
D. Reject the null hypothesis because u=35.1 million shares does not fall in the confidence interval.