Question

The average daily volume of a computer stock in 2011 was h=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 30.1 million​ shares, with a standard deviation of s=14.3 million shares. Test the hypotheses by constructing a 95​% confidence interval. Complete parts​ (a) through​ (c) below.

Answer 1

One-Sample t-test Confidence Interval

The provided sample mean is Xˉ=30.1 and the sample standard deviation is s=14.3. The size of the sample is n = 40 and the required confidence level is 95%. Degree of freedom The number of degrees of freedom are df = 40 - 1 = 39, and the significance level is α=0.05. Critical Value Based on the provided information, the critical t-value for α=0.05 and df=39 degrees of freedom is tc​=2.0227. Margin of Error Therefore, based on the information provided, the 95% confidence for the population mean μ is calculated as: Therefore, the 95% confidence interval for the population mean μ is 25.5266<μ<34.6734, which indicates that we are 95% confident that the true population proportion μ is contained by the interval (25.5266,34.6734)

Since 35.1 is not contained in the above 95% confidence interval, we can say that there is sufficient evidence to support the hypothesis that the stock volume in 2014 is different from the 2011 level.

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