Question

The average daily volume of a computer stock in 2011 was ų=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 32.7 million shares, with a standard deviation of s=14.6 million shares. Test the hypothesis by constructing a 95% confidence interval. Complete a and b A. State the hypothesis B. Construct a 95% confidence interval about the sample mean of stocks traded in 2014.

Answer 1

a

The null hypothesis is
`H_o : \mu = 35 .1 \ million \ shares`

The alternative hypothesis
`H_a : \mu \\e 35.1\ million \ shares`

b

The 95% confidence interval is
`27.475 < \mu < 37.925`

Explanation:

From the question the we are told that

The population mean is
`\mu = 35.1 \ million \ shares`

The sample size is n = 30

The sample mean is
`\= x = 32.7 \ million\ shares`

The standard deviation is
`\sigma = 14.6 \ million\ shares`

Given that the confidence level is
`95\%` then the level of significance is mathematically represented as

`\alpha = 100-95`

`\alpha = 5\%`

=>
`\alpha = 0.05`

Next we obtain the critical value of
`(\alpha )/(2)` from the normal distribution table

The value is
`Z_{(\alpha )/(2) } = 1.96`

Generally the margin of error is mathematically represented as

`E = Z_{(\alpha )/(2) } * ( \sigma )/(√(n) )`

substituting values

`E = 1.96 * ( 14.6 )/(√(30) )`

`E = 5.225`

The 95% confidence interval confidence interval is mathematically represented as

`\= x -E < \mu < \= x +E`

substituting values

`32.7 - 5.225 < \mu < 32.7 + 5.225`

`27.475 < \mu < 37.925`