Question

The average daily volume of a computer stock in 2011 was μ=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 30 trading days in​ 2014, he finds the sample mean to be 26.5 million​ shares, with a standard deviation of s= 14 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.

Lower bound = (BLANK)

Upper bound = (BLANK)

(c) Will the researcher reject the null hypothesis?

Answer 1

H0: = 35.1

Ha: 35.1

b)

95% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.05 /2, 30- 1 ) = 2.045
26.5 ± t(0.05/2, 30 -1) * 14/√(30)
Lower Limit = 26.5 - t(0.05/2, 30 -1) 14/√(30)
Lower Limit = 21.2729
Upper Limit = 26.5 + t(0.05/2, 30 -1) 14/√(30)
Upper Limit = 31.7271

C)

Since true mean 35.1 is outside the confidnece interval, Reject the null hypothesis.