Question

Jessica knows that the adult population gets, on average, eight hours of sleep each night. A hypothesis test can help her see if college students are different from the adult population.

Jessica tabulated that her sample of 101 students got an average of 6.9 hours of sleep each night, with a standard deviation of 2.5.

Using the data provided and the formula below, what is the t-statistic that Jessica calculates? Answer choices are rounded to the hundredths place.

Answer 1

Given that

population mean \(\mu=8\)

sample mean \(\bar{x}=6.9\) standar d deviation \(s=2.5\)

size \(n=101\)

test statistic \(t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}\)

\(=\frac{6.9-8}{\frac{2.5}{\sqrt{101}}}\)

\(=-1.1 / 0.2487593\)

\(=-4.42\)