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 2018 is different from the 2011 level. Based on a random sample of 40 trading days in​ 2018, he finds the sample mean to be 31.8 million​ shares, with a standard deviation of s=14.6 million shares. Test the hypotheses by constructing a 95​% confidence interval.

​(a) State the hypotheses for the test.
(b) Determine if the researcher will reject the null hypothesis.

Answer 1

The 95% confidence interval is ( 27.126 , 34.674)

Explanation:

Given

The t critical value at 0.05 level = 2.023 for the df = 39

Confidence interval = 95%

Mean

`\bar{x} - t * (s)/(√(n) ) < \mu < \bar{x} + t * (s)/(√(n) )`

Substituting the given values we get -

`\30.9 - 2.023 * (11.8)/(√(40) ) < \mu < \30.9 + 2.023 * (11.8)/(√(40) )\\27.126 < \mu < 34.674`

Hence, the 95% confidence interval is

( 27.126 , 34.674)